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### Nyquist Didn't Say That

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Kinda off topic --

A month or two ago there was a spate of postings on these groups
displaying a profound misunderstanding of how to apply Nyquist's theorem
to problems of setting sampling or designing anti-alias filters.  I
helped folks out as much as I could, but it really demands an article,
which I am currently working on.

The misconceptions that I noticed pretty much boiled down to the
following two:

One, "I need to monitor a signal that happens at X Hz, so I'm going to
sample it at 2X Hz".

Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
with a cutoff of X/2 Hz".

I estimate that answering these misconceptions will only take 3-4k
words, but I don't want to miss any other big ones.

Have you seen any other real howlers that relate to Nyquist, and what
you should really be thinking about when you're pondering sampling
rates, anti-aliasing filters and/or reconstruction filters?

Danke.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 0
Reply tim177 (4434) 8/22/2006 10:23:14 PM

See related articles to this posting

Tim Wescott wrote:
> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I
> helped folks out as much as I could, but it really demands an article,
> which I am currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k
> words, but I don't want to miss any other big ones.
>
> Have you seen any other real howlers that relate to Nyquist, and what
> you should really be thinking about when you're pondering sampling
> rates, anti-aliasing filters and/or reconstruction filters?
>
> Danke.

So, if you need to monitor a signal that occurs at xHz - what frequency
should you sample it at?

D

 0
Reply dave6855 (27) 8/22/2006 10:31:53 PM

Tim Wescott wrote:

> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
looks ok to me and Mr Nyquist, I suspect, ...what do you think the
relationships should be


 0
Reply bungalow_steve (615) 8/22/2006 10:36:47 PM

Tim Wescott wrote:
> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I
> helped folks out as much as I could, but it really demands an article,
> which I am currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k
> words, but I don't want to miss any other big ones.
>
> Have you seen any other real howlers that relate to Nyquist, and what
> you should really be thinking about when you're pondering sampling
> rates, anti-aliasing filters and/or reconstruction filters?

Before going into a detailed article, perhaps
you could review/improve the wikipedia article:

http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem


 0
Reply jstewart1 (739) 8/22/2006 10:43:08 PM

Tim Wescott said the following on 22/08/2006 23:23:
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".

Are you referring to:

a) bandpass sampling,
or
b) in baseband sampling, the notion that in practice, one needs to
sample faster than 2X Hz to measure something at X Hz?

(or both)?

--
Oli

 0
Reply catch (918) 8/22/2006 10:43:58 PM

steve wrote:
> Tim Wescott wrote:
>
>
>>One, "I need to monitor a signal that happens at X Hz, so I'm going to
>>sample it at 2X Hz".
>>
>>Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
>>with a cutoff of X/2 Hz".
>>
>
> looks ok to me and Mr Nyquist, I suspect, ...what do you think the
> relationships should be

I'd guess he wants the word "periodic" in there somewhere (:


 0
Reply jstewart1 (739) 8/22/2006 10:46:04 PM

Oli Filth wrote:

> Tim Wescott said the following on 22/08/2006 23:23:
>
>> The misconceptions that I noticed pretty much boiled down to the
>> following two:
>>
>> One, "I need to monitor a signal that happens at X Hz, so I'm going to
>> sample it at 2X Hz".
>>
>> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
>> with a cutoff of X/2 Hz".
>
>
> Are you referring to:
>
> a) bandpass sampling,

I doubt that I'm going to touch bandpass sampling, and if I do it'll be
using a 10 foot pole.

> or
> b) in baseband sampling, the notion that in practice, one needs to
> sample faster than 2X Hz to measure something at X Hz?
>
Yes, (b).  As well as the notion that just because your signal has a
fundamental frequency of X that doesn't mean it doesn't have harmonics
up as far as the imagination can reach.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 0
Reply tim177 (4434) 8/22/2006 10:46:32 PM

David Hearn wrote:

> Tim Wescott wrote:
>
>> Kinda off topic --
>>
>> A month or two ago there was a spate of postings on these groups
>> displaying a profound misunderstanding of how to apply Nyquist's
>> theorem to problems of setting sampling or designing anti-alias
>> filters.  I helped folks out as much as I could, but it really demands
>> an article, which I am currently working on.
>>
>> The misconceptions that I noticed pretty much boiled down to the
>> following two:
>>
>> One, "I need to monitor a signal that happens at X Hz, so I'm going to
>> sample it at 2X Hz".
>>
>> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
>> with a cutoff of X/2 Hz".
>>
>> I estimate that answering these misconceptions will only take 3-4k
>> words, but I don't want to miss any other big ones.
>>
>> Have you seen any other real howlers that relate to Nyquist, and what
>> you should really be thinking about when you're pondering sampling
>> rates, anti-aliasing filters and/or reconstruction filters?
>>
>> Danke.
>
>
> So, if you need to monitor a signal that occurs at xHz - what frequency
> should you sample it at?
>
> D

You need to be more than 2X times the highest interesting frequency
component in your periodic wave, which can be quite high in some cases.
You may also have to do some anti-alias filtering.

Or in other words "that depends".  Which is why I'm writing the dang
article, so I only have to write it once...

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 0
Reply tim177 (4434) 8/22/2006 10:49:15 PM

"Tim Wescott" <tim@seemywebsite.com> wrote in message
news:q6mdnZgxjJhQHnbZnZ2dnUVZ_rGdnZ2d@web-ster.com...
> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I helped
> folks out as much as I could, but it really demands an article, which I am
> currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the following
> two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k words,
> but I don't want to miss any other big ones.
>
> Have you seen any other real howlers that relate to Nyquist, and what you
> should really be thinking about when you're pondering sampling rates,
> anti-aliasing filters and/or reconstruction filters?
>
> Danke.
>
> --
>
> Tim Wescott
> Wescott Design Services
> http://www.wescottdesign.com
>

I have noticed that for switch mode power supplies the loop crossover
frequency is Fs/2piD and have often modelled such things in spice and they
have behaved themselves where the loop crossover frequency is well above a
half of Fs which rather pisses on Nyquist....

What did I miss?

DNA


 0
Reply mrspamizgood (17) 8/22/2006 10:50:24 PM

Tim,
are you going to be including in your artcle cases with filter banks,
specifically, critical sampled, oversampled etc, and how nyquist fits
into those implementations?

Tim Wescott wrote:
> David Hearn wrote:
>
> > Tim Wescott wrote:
> >
> >> Kinda off topic --
> >>
> >> A month or two ago there was a spate of postings on these groups
> >> displaying a profound misunderstanding of how to apply Nyquist's
> >> theorem to problems of setting sampling or designing anti-alias
> >> filters.  I helped folks out as much as I could, but it really demands
> >> an article, which I am currently working on.
> >>
> >> The misconceptions that I noticed pretty much boiled down to the
> >> following two:
> >>
> >> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> >> sample it at 2X Hz".
> >>
> >> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> >> with a cutoff of X/2 Hz".
> >>
> >> I estimate that answering these misconceptions will only take 3-4k
> >> words, but I don't want to miss any other big ones.
> >>
> >> Have you seen any other real howlers that relate to Nyquist, and what
> >> you should really be thinking about when you're pondering sampling
> >> rates, anti-aliasing filters and/or reconstruction filters?
> >>
> >> Danke.
> >
> >
> > So, if you need to monitor a signal that occurs at xHz - what frequency
> > should you sample it at?
> >
> > D
>
> You need to be more than 2X times the highest interesting frequency
> component in your periodic wave, which can be quite high in some cases.
>   You may also have to do some anti-alias filtering.
>
> Or in other words "that depends".  Which is why I'm writing the dang
> article, so I only have to write it once...
>
> --
>
> Tim Wescott
> Wescott Design Services
> http://www.wescottdesign.com
>
>
> "Applied Control Theory for Embedded Systems" came out in April.
> See details at http://www.wescottdesign.com/actfes/actfes.html


 0
Reply crroush (42) 8/22/2006 10:56:43 PM

David Hearn wrote:
> Tim Wescott wrote:
> > Kinda off topic --
> >
> > A month or two ago there was a spate of postings on these groups
> > displaying a profound misunderstanding of how to apply Nyquist's theorem
> > to problems of setting sampling or designing anti-alias filters.  I
> > helped folks out as much as I could, but it really demands an article,
> > which I am currently working on.
> >
> > The misconceptions that I noticed pretty much boiled down to the
> > following two:
> >
> > One, "I need to monitor a signal that happens at X Hz, so I'm going to
> > sample it at 2X Hz".
> >
> > Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> > with a cutoff of X/2 Hz".
> >
> > I estimate that answering these misconceptions will only take 3-4k
> > words, but I don't want to miss any other big ones.
> >
> > Have you seen any other real howlers that relate to Nyquist, and what
> > you should really be thinking about when you're pondering sampling
> > rates, anti-aliasing filters and/or reconstruction filters?
> >
> > Danke.
>
> So, if you need to monitor a signal that occurs at xHz - what frequency
> should you sample it at?
>
> D

a little over 2x the bandwidth of the signal should be sufficient,

-Lasse


 0

Jim Stewart wrote:

> Tim Wescott wrote:
>
>> Kinda off topic --
>>
>> A month or two ago there was a spate of postings on these groups
>> displaying a profound misunderstanding of how to apply Nyquist's
>> theorem to problems of setting sampling or designing anti-alias
>> filters.  I helped folks out as much as I could, but it really demands
>> an article, which I am currently working on.
>>
>> The misconceptions that I noticed pretty much boiled down to the
>> following two:
>>
>> One, "I need to monitor a signal that happens at X Hz, so I'm going to
>> sample it at 2X Hz".
>>
>> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
>> with a cutoff of X/2 Hz".
>>
>> I estimate that answering these misconceptions will only take 3-4k
>> words, but I don't want to miss any other big ones.
>>
>> Have you seen any other real howlers that relate to Nyquist, and what
>> you should really be thinking about when you're pondering sampling
>> rates, anti-aliasing filters and/or reconstruction filters?
>
>
> Before going into a detailed article, perhaps
> you could review/improve the wikipedia article:
>
> http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem
>
>
Because I'm a mercenary.

Posting to wikipedia doesn't pay directly, nor does it give me public
credit.  While it benefits the world it doesn't lead to me getting any
checks in the mail.

By contrast I can contribute to newsgroups, post articles on my website,
or sell articles to trade magazines.  Each one of these activities binds
my name to the knowledge*, gives it distribution to the english speaking
world to one extent or another, gives me a reasonable chance of having
my name pop up on a web search, and should it get bought by a magazine
I'll get almost 1/10th of minimum wage for the effort I've put into it.
As a consequence, folks who need to know how to do the stuff I write
about see me as a potential resource when they go looking for consultants.

Until I win the lottery or retire I can't afford to spend the time on
anonymous contributions to Wikis.

* Hopefully that's a good thing.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 0
Reply tim177 (4434) 8/22/2006 11:09:13 PM

Tim,

"Tim Wescott" <tim@seemywebsite.com> wrote in message
news:hrGdnX1RNLcIE3bZnZ2dnUVZ_omdnZ2d@web-ster.com...
> Posting to wikipedia doesn't pay directly, nor does it give me public
> credit.  While it benefits the world it doesn't lead to me getting any
> checks in the mail.

Perhaps you'd be willing to take your articles and post them on Wikipedia as
well as the places where your name is directly tied to it (in a slightly
modified form)?  That way you'd help the public at large (it's a lot easier to
find things on Wikipedia than trying to search through a dozen technical
journals), and anyone who actually *has* money to pay will still find you.

---Joel


 0

langwadt@ieee.org wrote:
> David Hearn wrote:
> > Tim Wescott wrote:
> > > Kinda off topic --
> > >
> > > A month or two ago there was a spate of postings on these groups
> > > displaying a profound misunderstanding of how to apply Nyquist's theorem
> > > to problems of setting sampling or designing anti-alias filters.  I
> > > helped folks out as much as I could, but it really demands an article,
> > > which I am currently working on.
> > >
> > > The misconceptions that I noticed pretty much boiled down to the
> > > following two:
> > >
> > > One, "I need to monitor a signal that happens at X Hz, so I'm going to
> > > sample it at 2X Hz".
> > >
> > > Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> > > with a cutoff of X/2 Hz".
> > >
> > > I estimate that answering these misconceptions will only take 3-4k
> > > words, but I don't want to miss any other big ones.
> > >
> > > Have you seen any other real howlers that relate to Nyquist, and what
> > > you should really be thinking about when you're pondering sampling
> > > rates, anti-aliasing filters and/or reconstruction filters?
> > >
> > > Danke.
> >
> > So, if you need to monitor a signal that occurs at xHz - what frequency
> > should you sample it at?
> >
> > D
>
> a little over 2x the bandwidth of the signal should be sufficient,

Depending on what you want to do. And you'd better make sure that your
sampling points aren't 180 degrees apart wrt to the signal frequency
you want to sample.

--
Bill Sloman, Nijmegen


 0
Reply bill.sloman (95) 8/22/2006 11:19:53 PM

Joel Kolstad wrote:

> Tim,
>
> "Tim Wescott" <tim@seemywebsite.com> wrote in message
> news:hrGdnX1RNLcIE3bZnZ2dnUVZ_omdnZ2d@web-ster.com...
>
>>Posting to wikipedia doesn't pay directly, nor does it give me public
>>credit.  While it benefits the world it doesn't lead to me getting any
>>checks in the mail.
>
>
> Perhaps you'd be willing to take your articles and post them on Wikipedia as
> well as the places where your name is directly tied to it (in a slightly
> modified form)?  That way you'd help the public at large (it's a lot easier to
> find things on Wikipedia than trying to search through a dozen technical
> journals), and anyone who actually *has* money to pay will still find you.
>
> ---Joel
>
>
I may do that.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 0
Reply tim177 (4434) 8/22/2006 11:28:47 PM


Tim Wescott wrote:

>>> Have you seen any other real howlers that relate to Nyquist, and what
>>> you should really be thinking about when you're pondering sampling
>>> rates, anti-aliasing filters and/or reconstruction filters?

Recently I run into a problem with the digital PLL occasionally locking
on the aliased frequencies. The problem happens when the signal
constellation has N phase angles. That multiplies the difference phase
by N. Thus the error frequency may appear to be higher then baudrate/2,
causing all kinds of problems. Special care has to be taken to avoid this.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

 0
Reply antispam_bogus (2949) 8/22/2006 11:37:51 PM

Tim Wescott <tim@seemywebsite.com> wrote in
news:q6mdnZgxjJhQHnbZnZ2dnUVZ_rGdnZ2d@web-ster.com:

> Have you seen any other real howlers that relate to Nyquist, and what
> you should really be thinking about when you're pondering sampling
> rates, anti-aliasing filters and/or reconstruction filters?
>

Leave plenty of headroom is the motto.  These days, with disk space
around a buck per Gig, and communication protocols that sling data from
embedded systems to where they need to be very quickly, sample faster
than you need to.  Having a sample rate that's too fast could cause
problems with digital filter design down the road a ways, but it a
helluva lot easier to downsample later then to find out later you haven't
sampled fast enough and lost data integrity.  If it's important, filter
if you need to.  For about $100/channel, you can get nifty 8-pole Bessels that have pretty linear phase in the pass band. Personally, Im big on anti-aliasing filtering. I do pretty low frequency physiological stuff, and by matter of course I filter with 8 poles at 200Hz and sample at 500. But, people should be aware that anti-aliasing filtering is no magic bullet, and can be worthless if you design something wrong, like if you introduce ground loops or somehow push noise into the system after the filters. Anti-aliasing countermeasures begin with careful analog design to keep high frequency noise out of the system-- shields, good grounding schemes, correct bypassing, etc. Even with care, this can get nasty if you're driving real loads, like motors. I've toyed around with the whacked out idea of entirely isolating data acquisition and prefiltering from everything else, with isolating DC/DC converter or isolation transformers, and linear optical isolators on every analog input or output, and plain old optical isolators on every digital line. This design got expensive quickly, and its almost guaranteed to fail when someone new tries to expand your system. The more headroom in Nyquist you can afford to have, the less money you'll need to spend on your anti-aliasing filters, because the rolloff can be more gentle--sort of like how oversampling digital music makes the output filter cheaper. The choice of filter family is also a design parameter that might depend on good ol' Nyquist. If you're keeping things loose, you can choose a filter that doesn't drop like a hot rock, like a Bessel or Butterworth, but if you need to tighten things up, you need a Chebyshev or some such. That brings up another issue: anti-alias filtering is not free--clearly from a cost perspective, but you also need to deal with time delays and small passband gain fluctuation for Bessel Filters, passband phase distortion problems for Butterworth (and maybe a lower cutoff frequency to help with the slow rolloff), and phase and gain problems for the chebyshevs, when you need really fast rolloffs. I've also thought about actually doing silly things, like using dsp's to sample superfast with cheap analog filters on the inputs, and then doing the real filtering digitally, spitting the results out on DACs, and then resampling for storage. This seems real odd, but push comes to shove, it might be cheaper than$100 per channel for good analog filters.  But, it
doesn't really make sense-- you could just use the base system to
oversample like mad, filter, and decimate prior to storage.

Sorry for the ramble, Tim.  It's a little late for me to be forming
replies like this.

--
Scott

 0
Reply namdiesttocs (1202) 8/23/2006 12:21:29 AM

Tim Wescott wrote:
> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I
> helped folks out as much as I could, but it really demands an article,
> which I am currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>

Nyquist said that you need to sample at least 2X Bandwidth of the
signal to accurately reconstruct that signal. This is often miss-quoted
because in control system or some  other applications the bandwidth
goes down to dc so we are quote 2X highest freq of interest.

Of course due to other problems (not going into them here) we need to
sample about 5 to 10 times higher where feedback is involved.

S.


 0
Reply sheepshaggerx (35) 8/23/2006 12:37:16 AM

*** top posting fixed ***
decious wrote:
> Tim Wescott wrote:
>> David Hearn wrote:
>>> Tim Wescott wrote:
>>>
>>>> A month or two ago there was a spate of postings on these groups
>>>> displaying a profound misunderstanding of how to apply Nyquist's
>>>> theorem to problems of setting sampling or designing anti-alias
>>>> filters.  I helped folks out as much as I could, but it really
>>>> demands an article, which I am currently working on.
>>>>
>>>> The misconceptions that I noticed pretty much boiled down to the
>>>> following two:
>>>>
>>>> One, "I need to monitor a signal that happens at X Hz, so I'm
>>>> going to sample it at 2X Hz".
>>>>
>>>> Two, "I can sample at X Hz, so I'm going to build an anti-alias
>>>> filter with a cutoff of X/2 Hz".
>>>>
>>>> I estimate that answering these misconceptions will only take
>>>> 3-4k words, but I don't want to miss any other big ones.
>>>>
>>>> Have you seen any other real howlers that relate to Nyquist,
>>>> and what you should really be thinking about when you're
>>>> pondering sampling rates, anti-aliasing filters and/or
>>>> reconstruction filters?
>>>
>>> So, if you need to monitor a signal that occurs at xHz - what
>>> frequency should you sample it at?
>>
>> You need to be more than 2X times the highest interesting
>> frequency component in your periodic wave, which can be quite
>> high in some cases.  You may also have to do some anti-alias
>> filtering.
>>
>> Or in other words "that depends".  Which is why I'm writing the
>> dang article, so I only have to write it once...
>
> are you going to be including in your artcle cases with filter
> banks, specifically, critical sampled, oversampled etc, and how
> nyquist fits into those implementations?

Don't top-post.  It is rude and contravenes the standard practices
in newsgroups.  Your response belongs below, or intermixed with,
the *snipped* material you quote.  See the links in my sig. below.

The thing to remember about alias filtering is the word alias.  The
point is to remove incoming signals that can create false, or
alias, signals in the output.  No alias filter can really be an
instantaneous cutoff, so you have to ensure that aliasing noise is
sufficiently attenuated to not affect the actual response.  At the
same time all filters have effects on the time delay at various
frequencies, or phase response.  Linear phase filters, or constant
delay filters, have much less sharp cutoffs than may be desirable.

As ever, the task of the engineer is to make suitable compromises
between performance and cost.  There is nothing magic about the
word Nyquist - it is purely a theoretical limit.

I imagine these are the sort of things Tim will address.

future.  It will make life easier for all.

--
news:news.announce.newusers
http://www.geocities.com/nnqweb/
http://www.catb.org/~esr/faqs/smart-questions.html
http://www.caliburn.nl/topposting.html
http://www.netmeister.org/news/learn2quote.html


 0
Reply cbfalconer (19194) 8/23/2006 12:44:57 AM

Tim Wescott wrote:
> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I
> helped folks out as much as I could, but it really demands an article,
> which I am currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k
> words, but I don't want to miss any other big ones.
>
> Have you seen any other real howlers that relate to Nyquist, and what
> you should really be thinking about when you're pondering sampling
> rates, anti-aliasing filters and/or reconstruction filters?
>
> Danke.

A couple of others have mentioned this already, but the bandwidth vs
highest frequency issue does come to mind.

Rune


 0
Reply allnor (8506) 8/23/2006 1:02:31 AM

Vladimir Vassilevsky wrote:
>
>
> Tim Wescott wrote:
>
>
>
>>>> Have you seen any other real howlers that relate to Nyquist, and
>>>> what you should really be thinking about when you're pondering
>>>> sampling rates, anti-aliasing filters and/or reconstruction filters?
>
> Recently I run into a problem with the digital PLL occasionally locking
> on the aliased frequencies. The problem happens when the signal
> constellation has N phase angles. That multiplies the difference phase
> by N. Thus the error frequency may appear to be higher then baudrate/2,
> causing all kinds of problems. Special care has to be taken to avoid this.

Isn't that just the generic issue that after sampling you'd better make
sure your algorithms don't result in any frequency multiplication? If
they do, you'll fatten the bandwidth and be in trouble.

Regards,
Steve

 0
Reply steveu (1008) 8/23/2006 1:25:05 AM

You should discuss the question of whether it is possible to remove
unwanted aliased-in noise by clever digital filtering in a downstream
calculation.  In my understanding this is not possible.  But maybe I
slept through that part of the class.

You should discuss what happens to a signal that is filtered and sampled
in one system at rate X, but is transmitted to a receiving system at
update rate Y, then used by that receiving system at rate Z.  How should
one select the analog anti-aliasing filter in this situation?

mw

 0
Reply mw9936 (11) 8/23/2006 1:27:36 AM

On Tue, 22 Aug 2006 23:31:53 +0100, David Hearn <dave@NOswampieSPAM.org.uk>
wrote:

>Tim Wescott wrote:
>> Kinda off topic --
>>
>> A month or two ago there was a spate of postings on these groups
>> displaying a profound misunderstanding of how to apply Nyquist's theorem
>> to problems of setting sampling or designing anti-alias filters.  I
>> helped folks out as much as I could, but it really demands an article,
>> which I am currently working on.
>>
>> The misconceptions that I noticed pretty much boiled down to the
>> following two:
>>
>> One, "I need to monitor a signal that happens at X Hz, so I'm going to
>> sample it at 2X Hz".
>>
>> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
>> with a cutoff of X/2 Hz".
>>
>> I estimate that answering these misconceptions will only take 3-4k
>> words, but I don't want to miss any other big ones.
>>
>> Have you seen any other real howlers that relate to Nyquist, and what
>> you should really be thinking about when you're pondering sampling
>> rates, anti-aliasing filters and/or reconstruction filters?
>>
>> Danke.
>
>So, if you need to monitor a signal that occurs at xHz - what frequency
>should you sample it at?

Consider anything *other than* a pure sine wave at x Hz.  Consider say a square
wave at x Hz, sampled at 2x Hz.  What do *you* envisage those sample will let
you reconstruct?

 0
Reply me4 (19675) 8/23/2006 1:29:18 AM

langwadt@ieee.org wrote:

..

> a little over 2x the bandwidth of the signal should be sufficient,

Sometimes. If it's a closed-loop servo, maybe 5X oversampling is called
for. I've written about why before. It's enough to say here that one
sample delay is 180 degrees phase shift at the sampling frequency.
Anti-alias filters have delays of their own. Sampling at 10 or 20 x can
avoid the need for an anti-alias filter altogether. "It depends."

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/23/2006 3:03:04 AM

Genome wrote:

...

> I have noticed that for switch mode power supplies the loop crossover
> frequency is Fs/2piD and have often modelled such things in spice and they
> have behaved themselves where the loop crossover frequency is well above a
> half of Fs which rather pisses on Nyquist....
>
> What did I miss?

Spice models continuous systems. Isn't the iteration interval
dynamically adjusted to be at least as small as needed?

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/23/2006 3:09:23 AM

rebel wrote:
> Consider anything *other than* a pure sine wave at x Hz.  Consider say a
> square  wave at x Hz, sampled at 2x Hz.  What do *you* envisage
> those sample will   let you reconstruct?

And the frequency of a square wave is what?
Hint, read up on Fourier series.

Sigh.
A square wave has infinite frequency, so what sample rate
do you propose?

All real signals are composites of sine waves in theory.
In practice, they usually don't have infinite numbers of composite
waves at infinite bandwidth.

BTW, a square wave can usually be expressed in four or six bytes.
just encode "squarewave, 10hz, 2 volt" and you are done.

--


 0
Reply none9134 (6) 8/23/2006 3:28:19 AM

On Tue, 22 Aug 2006 23:28:19 -0400, Pat Farrell <none@nospam.info> wrote:

>rebel wrote:
>> Consider anything *other than* a pure sine wave at x Hz.  Consider say a
>> square  wave at x Hz, sampled at 2x Hz.  What do *you* envisage
>> those sample will   let you reconstruct?
>
>And the frequency of a square wave is what?
>Hint, read up on Fourier series.

I'm fully aware of that, but thanks for passing the tip on for others.  That WAS
why I posed the question that way.

>Sigh.
>A square wave has infinite frequency, so what sample rate
>do you propose?
>
>All real signals are composites of sine waves in theory.
>In practice, they usually don't have infinite numbers of composite
>waves at infinite bandwidth.

Of course they don't, but the fourier series illustrates the point - the need to
sample at least twice per period of the highest frequency component present (in
a significant enough amplitude to matter wrt the sampling step)

>BTW, a square wave can usually be expressed in four or six bytes.
>just encode "squarewave, 10hz, 2 volt" and you are done.

For a sampling oscilloscope looking at an analog waveform, that isn't really
much help.

 0
Reply me4 (19675) 8/23/2006 4:14:07 AM

steve wrote:
> Tim Wescott wrote:
>
> > One, "I need to monitor a signal that happens at X Hz, so I'm going to
> > sample it at 2X Hz".
> >
> > Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> > with a cutoff of X/2 Hz".
> >
> looks ok to me

Does it?

>and Mr Nyquist, I suspect,

No.

> ...what do you think the
> relationships should be

a) Sample at Fs > 2X Hz
b) Cut-off at Fc < X/2 Hz

Note no equality signs here.

The sampling theorem states a *lower*bound* on the relation
between sampling frequency and the highest significant frequency
component in the signal.

There is nothing in the sampling theorem to suggest that
sampling at 2X Hz is *sufficient*.

Tiny detail in phrasing; huge difference in practice.

Rune


 0
Reply allnor (8506) 8/23/2006 4:38:53 AM

Tim Wescott wrote:
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k
> words, but I don't want to miss any other big ones.

Just tell them that they've got to make sure that they sample BELOW the
Nyquist frequency of the HIGHEST frequency present in the signal, and
that the cutoff frequency of a filter isn't the frequency at which the
output is effectively disappeared.

 0
Reply paul355 (411) 8/23/2006 7:27:25 AM

Tim Wescott wrote:

> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I
> helped folks out as much as I could, but it really demands an article,
> which I am currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k
> words, but I don't want to miss any other big ones.
>
> Have you seen any other real howlers that relate to Nyquist, and what
> you should really be thinking about when you're pondering sampling
> rates, anti-aliasing filters and/or reconstruction filters?
>
> Danke.
>
How about a few observable facts.
Like a signal at frequency F1 can be sampled at a rate F2 and the net
is the phase difference if these frequencies are *exactly* the same, or
if the ratio is exactly 1:2 or 2:1 or any other integer ratio.
If there is a slight difference in the ratio F1/F2 or F2/F1, that the
difference frequency is observable but no clue as to which one is the
least stable with short term measurements.

 0
Reply robertbaer (111) 8/23/2006 7:43:05 AM

Do consider this interesting (atleast for me) example

Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
i start sampling from time = 0. What would i get? Aint i statisifying
Nyquist here?

Regards

Tim Wescott wrote:
> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I
> helped folks out as much as I could, but it really demands an article,
> which I am currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k
> words, but I don't want to miss any other big ones.
>
> Have you seen any other real howlers that relate to Nyquist, and what
> you should really be thinking about when you're pondering sampling
> rates, anti-aliasing filters and/or reconstruction filters?
>
> Danke.
>
> --
>
> Tim Wescott
> Wescott Design Services
> http://www.wescottdesign.com
>
>
> "Applied Control Theory for Embedded Systems" came out in April.
> See details at http://www.wescottdesign.com/actfes/actfes.html


 0
Reply mobien (57) 8/23/2006 9:46:07 AM

In comp.arch.embedded,
mobi <mobien@gmail.com> wrote:
> Do consider this interesting (atleast for me) example
>
> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
> i start sampling from time = 0. What would i get? Aint i statisifying
> Nyquist here?

No you are not. You seemed to have missed Rune's post in this thread

--
Stef    (remove caps, dashes and .invalid from e-mail address to reply by mail)


 0
Reply stef33d (377) 8/23/2006 10:10:30 AM

"mobi" <mobien@gmail.com> wrote in message
> Do consider this interesting (atleast for me) example
>
> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
> i start sampling from time = 0. What would i get? Aint i statisifying
> Nyquist here?

bandwidth. I wish people would stop using this 'simplification' because the
less mathematically astute take it as true regardless because it seems so
reasonable. But reasonableness doesn't make things true. Its bandwidth,
bandwidth, BANDWIDTH that matters.

Now for the case at point. A pure sine wave has zero bandwidth by
definition. As such the lower bound on sampling rate is 0. Note that this is
the rate i.e samples per second. However, a few samples are needed to fix
starting phase, amplitude, and if a variable, the frequency. But this is not
a per-second requirement.

There is one complication, which is if the frequency is completely free then
the number of samples needed to determine the frequency is infinite (because
you could be sub-sampling). But if the frequency were completely free then
the 2X sampling frequency in the quote would also be infinite. Given an
upper bound on the frequency three (perfect) samples should be enough to fix
phase, amplitude and frequency.

So, again, remeber - bandwidth.

Peter


 0
Reply surname (86) 8/23/2006 10:31:48 AM

Tim Wescott wrote:
>
>> Tim,
>>
>> "Tim Wescott" <tim@seemywebsite.com> wrote in message
>> news:hrGdnX1RNLcIE3bZnZ2dnUVZ_omdnZ2d@web-ster.com...
>>
>>> Posting to wikipedia doesn't pay directly, nor does it give me public
>>> credit.  While it benefits the world it doesn't lead to me getting
>>> any checks in the mail.
>>
>>
>>
>> Perhaps you'd be willing to take your articles and post them on
>> Wikipedia as well as the places where your name is directly tied to it
>> (in a slightly modified form)?  That way you'd help the public at
>> large (it's a lot easier to find things on Wikipedia than trying to
>> search through a dozen technical journals), and anyone who actually
>> *has* money to pay will still find you.
>>
>> ---Joel
>>
>>
> I may do that.
>

Does Wikipedia have a posting mode that allow only original author or a
"approved" contributor to modify an article. I heard a recent story of
inserted.

Might the best approach be using "External links"?
Tim keeps control.
The "world" gets the information.
If Tim gets paid for the article, the publisher gets site exposure.

 0
Reply rowlett10 (1881) 8/23/2006 11:28:00 AM

Stef wrote:
> In comp.arch.embedded,
> mobi <mobien@gmail.com> wrote:
> > Do consider this interesting (atleast for me) example
> >
> > Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
> > i start sampling from time = 0. What would i get? Aint i statisifying
> > Nyquist here?
>
> No you are not. You seemed to have missed Rune's post in this thread
> about '=' vs ' >'.

Well, if you can guarantee that the cos has no phase shift, then you
may have a cos term at Nyquist frequency in discrete periodic sequences
without introducing aliasing ambiguity. OTH, any periodic, discrete
sequence with Nyquist frequency will be interepreted as a cos (zero
phase shift) by the discrete Fourier sum (aka DFT).

For example, the sequence

...., 1, -1, 1, -1, ...

will be interpreted as a cos with amplitude 1 by any (finite) DFT. The
sequence

...., 1/sqrt(2), -1/sqrt(2), 1/sqrt(2), ...

will be interpreted as a cos with amplitude 1/sqrt(2) as opposed to a
unit amplitude cos with pi/4 phase shift. By defintion, the imaginary
part of the Nyquist DFT coefficient is always zero for real sequences
(just as for the DC coefficient, but we don't want to discuss phase
shifts for DC signals again :-).

Regards,
Andor


 0
Reply andor.bariska (1307) 8/23/2006 12:50:21 PM


mobi wrote:
>
> Do consider this interesting (atleast for me) example
>
> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
> i start sampling from time = 0. What would i get?

In theory you get nothing. In practice you get a good indication of just
how non-linear and inaccurate your signal and sampling system really
are.

-jim

----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==----
http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups
----= East and West-Coast Server Farms - Total Privacy via Encryption =----

 0
Reply m3740 (420) 8/23/2006 1:18:46 PM

Tim Wescott wrote:
> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I
> helped folks out as much as I could, but it really demands an article,
> which I am currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k
> words, but I don't want to miss any other big ones.
>
> Have you seen any other real howlers that relate to Nyquist, and what
> you should really be thinking about when you're pondering sampling
> rates, anti-aliasing filters and/or reconstruction filters?
>
> Danke.
>
> --
>
> Tim Wescott
> Wescott Design Services
> http://www.wescottdesign.com
>
>
> "Applied Control Theory for Embedded Systems" came out in April.
> See details at http://www.wescottdesign.com/actfes/actfes.html
More quantitatively, the various questions about anti-alias and
sampling can be answered by reconstructing the signal from the proposed
signal system and them computing the error for antcipated input signals
by taking the difference (in simple systems).  Put another way, model
the signal processing path and compare it to what you want, to see if
the approximations you make in your implementation matter.  This
provides guidance for sampling rates and anti-aliasing; vesus various
input spectra/signals.  In signal processing we typically approximate
perfection (which is sometimes impossible) by various means; the
adequacy depends upon the errors that we allow.  Given a description of
what we want and a proposed implementation the errors should be
calculable.  Nyquist moerely talks about what can be made to wrk given
perfect resources; reconstruction of an incoming signal of a certain
type.  If you feed >2X  signals or don't reconstruct/use the data
optimally, you have to do the error analysis to see how much you are
paying for not being perfect.
In other words, you allways have to do an error calculation for an
proposed design and enviroment.

Ray

Ray


 0
Reply rerogers (26) 8/23/2006 1:31:17 PM

Rune Allnor wrote:
> steve wrote:
> > Tim Wescott wrote:
> >
> > > One, "I need to monitor a signal that happens at X Hz, so I'm going to
> > > sample it at 2X Hz".
> > >
> > > Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> > > with a cutoff of X/2 Hz".
> > >
> > looks ok to me
>
> Does it?
>
> >and Mr Nyquist, I suspect,
>
> No.
>
> > ...what do you think the
> > relationships should be
>
>
> a) Sample at Fs > 2X Hz
> b) Cut-off at Fc < X/2 Hz
>
> Note no equality signs here.
>
Well yes, but that is only due to the fact if you sample at exactly 2x
you might sample at the zero points of the the sin wave, and not be
able to reproduce the signal, but most people write =2x because of
convenience, but if 2.0000000000001 is how you like to write it, then
ok.

> The sampling theorem states a *lower*bound* on the relation
> between sampling frequency and the highest significant frequency
> component in the signal.
>
> There is nothing in the sampling theorem to suggest that
> sampling at 2X Hz is *sufficient*.
>
> Tiny detail in phrasing; huge difference in practice.
>
> Rune


 0
Reply bungalow_steve (615) 8/23/2006 1:45:29 PM

sample and hold circuit needs sample interval more than twice frequency
of sample, but lower frequency sampling can be done if more than two
samplings is happening.

eg 1024Hz and 125HzHz => max freq descrimination = 2^10*5^3 Hz

cheers


 0
Reply jackokring (1001) 8/23/2006 1:45:40 PM


Tim Wescott wrote:

>>
> Because I'm a mercenary.
>
> Posting to wikipedia doesn't pay directly, nor does it give me public
> credit.  While it benefits the world it doesn't lead to me getting any
> checks in the mail.

I share that pure cynical point of view and consider myself as a kind of
whore also :)))) Good luck.

Here is another tip:

What is generally referred as "sampling" actually consists of two
different processes rather then one:

1. Continuos time non-linear quantization of the amplitude
2. Linear quantization in time

This representation clarifies many issues such as "quantization noise",
why the high sample rates are required, etc.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com


 0
Reply antispam_bogus (2949) 8/23/2006 1:49:40 PM

Tim Wescott wrote:
> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.

After reading some of the contributions to this thread, I can see that
you were right.


 0

steve wrote:

...

> Well yes, but that is only due to the fact if you sample at exactly 2x
> you might sample at the zero points of the the sin wave, and not be
> able to reproduce the signal, but most people write =2x because of
> convenience, but if 2.0000000000001 is how you like to write it, then
> ok.

No; it's more than that. It means (among other problems) that there's no
way to determine the component in phase with the sample clock (sine
component), so the amplitude remains unknown.

That's the least of the problems, though. To resolve a frequency of f
Hz, one must sample on the order of 1/f seconds. Frequencies in the
sampled domain lie on a circular scale, so that it is also necessary to
sample on the order of 1/f seconds to resolve a frequency of Fs/2 - f.

We can no more sample frequencies close to Fs/2 in a reasonably short
time than we can those close to DC.

So many misconceptions, so little time. Tim: are you tuned in?

To the person who wondered if he had been asleep in class when the way
to remove aliases after sampling was explained: you didn't miss a thing.
Think of the original components as sticks of varying lengths. (The
lengths are proportional to frequency.) The sampling process chops up
any length greater than Fs/2 into pieces of length Fs/2 which it
discards, and leaves the remainder in the pile. The result is that all
the sticks are shorter than Fs/2, even though some *were originally*
part of longer sticks. There is absolutely no way to tell the original
length after the ax falls.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/23/2006 3:49:19 PM

jacko wrote:
> sample and hold circuit needs sample interval more than twice frequency
> of sample, but lower frequency sampling can be done if more than two
> samplings is happening.
>
> eg 1024Hz and 125HzHz => max freq descrimination = 2^10*5^3 Hz

You didn't quote context, so I don't know what you're driving at.
Whatever, I don't get it; can you add some meat to the bones?

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/23/2006 3:52:40 PM

mobi wrote:
> Do consider this interesting (atleast for me) example
>
> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
> i start sampling from time = 0. What would i get? Aint i statisifying
> Nyquist here?

Yes, you are. Your example shows that while satisfying the Nyquist
sampling criterion may be a necessary condition, it certainly isn't
sufficient. That's what some of us have been trying to get across.

...

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/23/2006 3:56:37 PM

Stef wrote:
> In comp.arch.embedded,
> mobi <mobien@gmail.com> wrote:
>> Do consider this interesting (atleast for me) example
>>
>> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
>> i start sampling from time = 0. What would i get? Aint i statisifying
>> Nyquist here?
>
> No you are not. You seemed to have missed Rune's post in this thread
> about '=' vs ' >'.

Equality is enough to avoid aliasing. The inequality is needed to enable
reconstruction. Don't ignore the needed sampling duration in the "almost
equal" case.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/23/2006 4:00:03 PM

Tim Wescott wrote:

> Kinda off topic --
>
> A month or two ago there was a spate of postings on these groups
> displaying a profound misunderstanding of how to apply Nyquist's theorem
> to problems of setting sampling or designing anti-alias filters.  I
> helped folks out as much as I could, but it really demands an article,
> which I am currently working on.
>
> The misconceptions that I noticed pretty much boiled down to the
> following two:
>
> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> sample it at 2X Hz".
>
> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> with a cutoff of X/2 Hz".
>
> I estimate that answering these misconceptions will only take 3-4k
> words, but I don't want to miss any other big ones.
>
> Have you seen any other real howlers that relate to Nyquist, and what
> you should really be thinking about when you're pondering sampling
> rates, anti-aliasing filters and/or reconstruction filters?
>
> Danke.
>

The other one I run into is that N. really applies to the bandwidth, not
the highest frequency as is commonly thought.  Harmonic mixers make use
of this all the time, using the equivalence of the sampled interval to
the fundamental interval [-f_s/2, f_s/2), and alias down to some lower
frequency in the process.  If you really reconstruct with impulses, you
can use a bandpass filter to get back the original signal at the
original carrier frequency.

People also routinely neglect the to account for the zero-order hold in
their DAC circuits--if you take a signal, run it through an A/D and a
D/A, you don't wind up with the original signal, but one with an

Cheers,

Phil Hobbs

 0
Reply pcdh1 (19) 8/23/2006 4:13:33 PM

Jerry Avins wrote:
> steve wrote:

> No; it's more than that. It means (among other problems) that there's no
> way to determine the component in phase with the sample clock (sine
> component), so the amplitude remains unknown.
>
sampling at 2.000001X solves that problem, there are no frequencies in
phase with the sample clock anymore, the point I was making

There is no additional information obtained by sampling at a higher
rate.

> That's the least of the problems, though. To resolve a frequency of f
> Hz, one must sample on the order of 1/f seconds.

doesn't make any sense to me, so to resolve a frequency of 10 hz one
must sample on the order of 1/10 seconds? Is that what you are saying,
or am I reading it wrong?

> So many misconceptions, so little time. Tim: are you tuned in?
>
Tim is making many assumptions (unfairly in my opinion) beforehand
about the signal and anti-alias filter in his original post, and then
saying this and that statement is not correct. Is he assuming
frequencies higher then the desired signal exist, I think so, but I
don't know, is he assuming a non-brick wall anti-alias filter? I think
so but who knows. Nyquist assumes the ideals, you can't have a theorem
otherwise.


 0
Reply bungalow_steve (615) 8/23/2006 5:39:59 PM

"steve" <bungalow_steve@yahoo.com> wrote in news:1156354799.705801.226400

> There is no additional information obtained by sampling at a higher
> rate.

No additional information, but its certainly easier to look at your data
when there's more than one point in each half cycle.

--
Scott

 0
Reply namdiesttocs (1202) 8/23/2006 5:52:01 PM

On Wed, 23 Aug 2006 12:13:33 -0400, Phil Hobbs
<pcdh@SpamMeSenseless.pergamos.net> wrote:

>Tim Wescott wrote:
>
>> Kinda off topic --
>>
>> A month or two ago there was a spate of postings on these groups
>> displaying a profound misunderstanding of how to apply Nyquist's theorem
>> to problems of setting sampling or designing anti-alias filters.  I
>> helped folks out as much as I could, but it really demands an article,
>> which I am currently working on.
>>
>> The misconceptions that I noticed pretty much boiled down to the
>> following two:
>>
>> One, "I need to monitor a signal that happens at X Hz, so I'm going to
>> sample it at 2X Hz".
>>
>> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
>> with a cutoff of X/2 Hz".
>>
>> I estimate that answering these misconceptions will only take 3-4k
>> words, but I don't want to miss any other big ones.
>>
>> Have you seen any other real howlers that relate to Nyquist, and what
>> you should really be thinking about when you're pondering sampling
>> rates, anti-aliasing filters and/or reconstruction filters?
>>
>> Danke.
>
>The other one I run into is that N. really applies to the bandwidth, not
>the highest frequency as is commonly thought.  Harmonic mixers make use
>of this all the time, using the equivalence of the sampled interval to
>the fundamental interval [-f_s/2, f_s/2), and alias down to some lower
>frequency in the process.  If you really reconstruct with impulses, you
>can use a bandpass filter to get back the original signal at the
>original carrier frequency.
>
>People also routinely neglect the to account for the zero-order hold in
>their DAC circuits--if you take a signal, run it through an A/D and a
>D/A, you don't wind up with the original signal, but one with an

This last paragraph seems worth emphasizing, particularly on the
subject of sampling rates, as it points out a reason why rather more
than 2.00...01 X sampling may be important.  I'm not sure how a
practical reconstruction filter to compensate for ZOH could be
arranged, causal or acausal, otherwise.  You need some margin for the
skirts, don't you?

Jon

>
>Cheers,
>
>Phil Hobbs


 0
Reply jkirwan (830) 8/23/2006 6:11:09 PM

Scott Seidman wrote:
> "steve" <bungalow_steve@yahoo.com> wrote in news:1156354799.705801.226400
>
> > There is no additional information obtained by sampling at a higher
> > rate.
>
> No additional information, but its certainly easier to look at your data
> when there's more than one point in each half cycle.
>
> --
Yes, easier to reconstruct a signal with more samples


 0
Reply bungalow_steve (615) 8/23/2006 6:14:53 PM

Tim Wescott wrote:
>>...
>> Perhaps you'd be willing to take your articles and post them on
>> Wikipedia as well as the places where your name is directly tied to it
>> (in a slightly modified form)?  That way you'd help the public at
>> large (it's a lot easier to find things on Wikipedia than trying to
>> search through a dozen technical journals), and anyone who actually
>> *has* money to pay will still find you.
>>
>> ---Joel
>>
>>
> I may do that.

Wikipedia articles often have external links, which people frequently
leave alone (IE don't vandalize). Just contribute *something* useful
to the wikipedia article, then link to your own area for in-depth
coverage. Win-win scenario.

I don't think Wikipedia's going away. I find myself using it more and
more as a first step to getting any info on some new subject -- even

Now here's a thought -- if Wikipedia can become financially
viable in its own right (currently it depends on donations) maybe a
business model can appear where based on number of "views" of
pages, the contributing authors can get some $$sent their way. Yes -- it's viable! #1) Suggest the possibility #2) ??? #3) Profit! -Dave   0 Reply dash (43) 8/23/2006 6:28:39 PM David Ashley said the following on 23/08/2006 19:28: > I don't think Wikipedia's going away. I find myself using it more and > more as a first step to getting any info on some new subject -- even > before google actually. In some areas, Wikipedia is great, in others it's dire (no disrepect intended to anyone that contributes, myself included). Articles about comms and signal processing (as relevant examples) are on the whole scant, badly written and error-prone. However, I'm sure this will change over time. > Now here's a thought -- if Wikipedia can become financially > viable in its own right (currently it depends on donations) maybe a > business model can appear where based on number of "views" of > pages, the contributing authors can get some$$$sent their > way. > > Yes -- it's viable! > > #1) Suggest the possibility > #2) ??? > #3) Profit! Nice idea, but I don't think it's ever going to happen. For one, the Wikipedia administrators are already working hard to reduce the systematic bias that exists in Wikipedia (see http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Countering_systemic_bias), introducing a financial incentive to writing good articles could only make this worse. -- Oli   0 Reply catch (918) 8/23/2006 6:46:07 PM On Wed, 23 Aug 2006 12:14:07 +0800, rebel <me@privacy.net> wrote: >On Tue, 22 Aug 2006 23:28:19 -0400, Pat Farrell <none@nospam.info> wrote: > >>rebel wrote: >>> Consider anything *other than* a pure sine wave at x Hz. Consider say a >>> square wave at x Hz, sampled at 2x Hz. What do *you* envisage >>> those sample will let you reconstruct? >> >>And the frequency of a square wave is what? >>Hint, read up on Fourier series. > >I'm fully aware of that, but thanks for passing the tip on for others. That WAS >why I posed the question that way. > >>Sigh. >>A square wave has infinite frequency, so what sample rate >>do you propose? >> >>All real signals are composites of sine waves in theory. >>In practice, they usually don't have infinite numbers of composite >>waves at infinite bandwidth. > >Of course they don't, but the fourier series illustrates the point - the need to >sample at least twice per period of the highest frequency component present (in >a significant enough amplitude to matter wrt the sampling step) > >>BTW, a square wave can usually be expressed in four or six bytes. >>just encode "squarewave, 10hz, 2 volt" and you are done. > >For a sampling oscilloscope looking at an analog waveform, that isn't really >much help. Again, "it depends". You really only need to sample 2x the bandwidth, as Nyquist stated, and in the case of something like a square wave one must determine the "bandwidth of interest", i.e., some point above which you're not interested or it won't matter. For sampled-IF (or super-Nyquist as some call it), one must pay attention to folding frequencies, etc. It's not hard to sort out, but I think an article like what is proposed is always a good thing, if well written, to clarify things and help folks avoid the pitfalls. Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org   0 Reply eric.jacobsen (2636) 8/23/2006 7:21:15 PM Jonathan Kirwan wrote: > This last paragraph seems worth emphasizing, particularly on the > subject of sampling rates, as it points out a reason why rather more > than 2.00...01 X sampling may be important. I'm not sure how a > practical reconstruction filter to compensate for ZOH could be > arranged, causal or acausal, otherwise. You need some margin for the > skirts, don't you? I used to work in an FFT factory, and we typically sampled at 2.56 x BW.   0 Reply pomerado (75) 8/23/2006 7:26:04 PM On Tue, 22 Aug 2006 15:46:32 -0700, Tim Wescott <tim@seemywebsite.com> wrote: >Oli Filth wrote: > >> Tim Wescott said the following on 22/08/2006 23:23: >> >>> The misconceptions that I noticed pretty much boiled down to the >>> following two: >>> >>> One, "I need to monitor a signal that happens at X Hz, so I'm going to >>> sample it at 2X Hz". >>> >>> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter >>> with a cutoff of X/2 Hz". >> >> >> Are you referring to: >> >> a) bandpass sampling, > >I doubt that I'm going to touch bandpass sampling, and if I do it'll be >using a 10 foot pole. Oh, in that case I'm not clear on where there's so much confusion that needs an entire article to clear up. I was hoping you'd hit the idea that Nyquist really said 2x the bandwidth of interest (as others have already mentioned). Clarifying that doesn't lose the context of baseband sampling, does address where the most common pitfalls lie, and provide a full treatment of the issue as well as covers what Nyquist really said. >> or >> b) in baseband sampling, the notion that in practice, one needs to >> sample faster than 2X Hz to measure something at X Hz? >> >Yes, (b). As well as the notion that just because your signal has a >fundamental frequency of X that doesn't mean it doesn't have harmonics >up as far as the imagination can reach. That's a fine notion to address, that all systems are essentially bandwidth limited by nature or can be made so easily. Tying that to the sampling rate is a fundamental issue, but I'm not certain that it can't be cleared up in a few well-written paragraphs with an illustration or two. But maybe I'm too optimistic... Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org   0 Reply eric.jacobsen (2636) 8/23/2006 7:28:02 PM steve wrote: > Jerry Avins wrote: >> steve wrote: > >> No; it's more than that. It means (among other problems) that there's no >> way to determine the component in phase with the sample clock (sine >> component), so the amplitude remains unknown. >> > sampling at 2.000001X solves that problem, there are no frequencies in > phase with the sample clock anymore, the point I was making > > There is no additional information obtained by sampling at a higher > rate. > >> That's the least of the problems, though. To resolve a frequency of f >> Hz, one must sample on the order of 1/f seconds. > > doesn't make any sense to me, so to resolve a frequency of 10 hz one > must sample on the order of 1/10 seconds? Is that what you are saying, > or am I reading it wrong? Right or wrong, that's what I meant.* What's more, to resolve Fs/2 - 10 Hz, you also need to to sample for a time in the order of 1/10 second. Why does it seem strange? >> So many misconceptions, so little time. Tim: are you tuned in? >> > Tim is making many assumptions (unfairly in my opinion) beforehand > about the signal and anti-alias filter in his original post, and then > saying this and that statement is not correct. Is he assuming > frequencies higher then the desired signal exist, I think so, but I > don't know, is he assuming a non-brick wall anti-alias filter? I think > so but who knows. Nyquist assumes the ideals, you can't have a theorem > otherwise. It seems to me that Tim is assuming anti-alias filters that produce results sooner than next week, and signals that would have components above Fs/2 without them. I don't think those assumptions are unfair. The Nyquist criterion does indeed assume ideal conditions. Tim will show that the assumption is rarely justified for real work. Jerry ___________________________________________ * Shorter time serves if you know more about your signal. If you know frequency, phase, and amplitude, no sampling is needed at all. If noise and quantization are insignificant and you know that only a single frequency is present, three samples suffice. If you know what that frequency is, two samples suffice. With most real-world conditions, you need about Fs * 10 samples. -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/23/2006 7:35:42 PM steve wrote: > Jerry Avins wrote: >> steve wrote: > >> No; it's more than that. It means (among other problems) that there's no >> way to determine the component in phase with the sample clock (sine >> component), so the amplitude remains unknown. >> > sampling at 2.000001X solves that problem, there are no frequencies in > phase with the sample clock anymore, the point I was making In theory only. To resolve a signal at 2.00000X would require 1,000,000 seconds. (OK: maybe only 150 hours.) > There is no additional information obtained by sampling at a higher > rate. True, but you can get that information a lot faster. >> That's the least of the problems, though. To resolve a frequency of f >> Hz, one must sample on the order of 1/f seconds. > > doesn't make any sense to me, so to resolve a frequency of 10 hz one > must sample on the order of 1/10 seconds? Is that what you are saying, > or am I reading it wrong? Right or wrong, that's what I meant.* What's more, to resolve Fs/2 - 10 Hz, you also need to to sample for a time in the order of 1/10 second. Why does it seem strange? >> So many misconceptions, so little time. Tim: are you tuned in? >> > Tim is making many assumptions (unfairly in my opinion) beforehand > about the signal and anti-alias filter in his original post, and then > saying this and that statement is not correct. Is he assuming > frequencies higher then the desired signal exist, I think so, but I > don't know, is he assuming a non-brick wall anti-alias filter? I think > so but who knows. Nyquist assumes the ideals, you can't have a theorem > otherwise. It seems to me that Tim is assuming anti-alias filters that produce results sooner than next week, and signals that would have components above Fs/2 without them. I don't think those assumptions are unfair. The Nyquist criterion does indeed assume ideal conditions. Tim will show that the assumption is rarely justified for real work. Jerry ___________________________________________ * Shorter time serves if you know more about your signal. If you know frequency, phase, and amplitude, no sampling is needed at all. If noise and quantization are insignificant and you know that only a single frequency is present, three samples suffice. If you know what that frequency is, two samples suffice. With most real-world conditions, you need about Fs * 10 samples. -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/23/2006 7:41:17 PM Tim Wescott wrote: > Have you seen any other real howlers that relate to Nyquist, and what > you should really be thinking about when you're pondering sampling > rates, anti-aliasing filters and/or reconstruction filters? it's not a howler, but the sampling frequency, Fs, must be strictly greater than twice the highest frequency, B, at least if that highest frequency is sinusoidal resulting in two dirac spikes at +/- B on the spectrum. the simplest way to say it is that Fs > 2*B the other thing i was gonna say is that at Wikipedia we are stuggling with some of this same stuff (what the Sampling Theorem, as commonly depicted in textbooks really says, the historic sampling theorem from Shannon is a bit different) and, perhaps, to avoid duplication of effort, you might want to jump into that fray instead. it's at: http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem i think there is some writing that craps up the article, but that is the lot and legacy of Wikipedia. an encyclopedia written by committee (the biggest, most inclusive committee possible). so "design by committee" is a problem. > Danke. Bitte. r b-j   0 Reply rbj (4087) 8/23/2006 8:07:40 PM Jerry Avins wrote: > In theory only. To resolve a signal at 2.00000X would require 1,000,000 > seconds. (OK: maybe only 150 hours.) 150 hours? Why? > Right or wrong, that's what I meant.* What's more, to resolve Fs/2 - 10 > Hz, you also need to to sample for a time in the order of 1/10 second. > Why does it seem strange? > 1/f is twice the nyquist time (1/2 the rate, undersampling) yet you seem to be implying oversampling   0 Reply bungalow_steve (615) 8/23/2006 8:14:45 PM Tim Wescott wrote: > Oli Filth wrote: > > > Tim Wescott said the following on 22/08/2006 23:23: > > > >> The misconceptions that I noticed pretty much boiled down to the > >> following two: > >> > >> One, "I need to monitor a signal that happens at X Hz, so I'm going to > >> sample it at 2X Hz". > >> > >> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter > >> with a cutoff of X/2 Hz". > > > > > > Are you referring to: > > > > a) bandpass sampling, > > I doubt that I'm going to touch bandpass sampling, and if I do it'll be > using a 10 foot pole. > > > or > > b) in baseband sampling, the notion that in practice, one needs to > > sample faster than 2X Hz to measure something at X Hz? > > > Yes, (b). As well as the notion that just because your signal has a > fundamental frequency of X that doesn't mean it doesn't have harmonics > up as far as the imagination can reach. but, Tim, the point is that you have to sample *faster* than 2X. sampling at 2X ain't good enough, even theoretically. sampling at 2.000001X might be good enough theoretically (the reconstruction filter will be a bitch) if acausality (or a long delay for the causal case) ain't a problem. the other thing to think about is that no D/A really outputs dirac impulses, so then something like a zero-order hold (ZOH) might have to be modeled for reasons of practicallity. lastly, even though we fight about a bunch of other things, i was surprized at the support i had at Wikipedia to include that "T factor" in the dirac comb sampling operator. putting it there and not in the passband gain of the reconstruction filter is dimensionally most appropriate and help set up the ZOH model without dropping the T factor (or going through a contorted argument for how to include it). i haven't read through this thread yet, so i apologize in advance if i am repeating someone else's words. r b-j   0 Reply rbj (4087) 8/23/2006 8:18:43 PM Jim Stewart wrote: > > Before going into a detailed article, perhaps > you could review/improve the wikipedia article: > > http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem i just came upon this. as one who has recently jumped into that fray, alls i can say is "HELP!". even if you lock horns with me, i would really like it if more comp.dspers would come to Wikipedia and contribute. someday, that can be the new FAQ, for *any* newsgroup. r b-j   0 Reply rbj (4087) 8/23/2006 8:23:32 PM robert bristow-johnson wrote: > .... snip ... > > but, Tim, the point is that you have to sample *faster* than 2X. > sampling at 2X ain't good enough, even theoretically. sampling at > 2.000001X might be good enough theoretically (the reconstruction > filter will be a bitch) if acausality (or a long delay for the > causal case) ain't a problem. the other thing to think about is > that no D/A really outputs dirac impulses, so then something like > a zero-order hold (ZOH) might have to be modeled for reasons of > practicallity. There is a world of difference between the output filters needed after a sample and hold, and after a quasi impulse function. Also in the gain needed. The impulse function has the advantage that several can be mixed. I took advantage of this in a PABX years ago to provide call merging. The actual pulses were about 1% of the repetition rate period. The accumulated DC components limited the merging to three calls. -- Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net) Available for consulting/temporary embedded and systems. <http://cbfalconer.home.att.net> USE maineline address!   0 Reply cbfalconer (19194) 8/23/2006 8:49:44 PM bungalow_steve@yahoo.com wrote: > Jerry Avins wrote: > >> In theory only. To resolve a signal at 2.00000X would require 1,000,000 >> seconds. (OK: maybe only 150 hours.) > > 150 hours? Why? A bad assumption on my part. 2.000001X isn't Hz; it needs to be normalized. The result is not a million seconds, but a million sample times. That's still a long time. Most of the time, there's pretty good resolution at half that, in this case, 500,000 sample times. >> Right or wrong, that's what I meant.* What's more, to resolve Fs/2 - 10 >> Hz, you also need to to sample for a time in the order of 1/10 second. >> Why does it seem strange? >> > 1/f is twice the nyquist time (1/2 the rate, undersampling) yet you > seem to be implying oversampling I don't see what you mean. Could you explain with an equation or two? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/23/2006 8:50:27 PM Jonathan Kirwan wrote: > ... You need some margin for the skirts, don't you? If course, and for other things too. Even if you can be certain that there is no signal energy above Fmax, you need to sample faster than 2Fmax in real situations. As it says on traffic a summons in Boston, "Fail ye not thereof at your peril." Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/23/2006 9:07:53 PM Eric Jacobsen wrote: > ... You really only need to sample 2x the > bandwidth, as Nyquist stated, and in the case of something like a > square wave one must determine the "bandwidth of interest", i.e., some > point above which you're not interested or it won't matter. C'mon, Eric; I know you know better. Either you sample so fast that significant aliases are higher than any component of interest (and so can be filtered digitally later) or you use an anti-alias filter so that in fact there's nothing to alias. > For sampled-IF (or super-Nyquist as some call it), one must pay > attention to folding frequencies, etc. Calling it "super Nyquist" reveals the ignorance that underlies the problem. > It's not hard to sort out, but I think an article like what is > proposed is always a good thing, if well written, to clarify things > and help folks avoid the pitfalls. Ja! Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/23/2006 9:15:17 PM "robert bristow-johnson" <rbj@audioimagination.com> wrote in news:1156363660.369874.238690@i3g2000cwc.googlegroups.com: > http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem > > i think there is some writing that craps up the article, but that is > the lot and legacy of Wikipedia. an encyclopedia written by committee > (the biggest, most inclusive committee possible). so "design by > committee" is a problem. > >> Danke. > > Bitte. > > r b-j > > Robert-- CommitteeSize = CommitteeSize + 1 ; %!!!!! I think what's missing is a demonstration that multiplication with the Dirac train in time pairs with convolution with the scaled Dirac in frequency. Without a good figure showing that, the figures under the "aliasing" subtitle lack some meaning. As an aside, I'm interested in the analogs in AM. By the book, the carrier needs to be twice as fast as the highest signal component, but for Hilbert demodulation, all I can find is the specification that the signal and carrier not overlap. Is this because the transform essentially throws out the negative frequencies, so you don't have to worry about positive/negative overlap? Alternatively, am I just wrong, and the carrier needs to be twice the highest frequency, even for Hilbert demod?? -- Scott Reverse name to reply   0 Reply namdiesttocs (1202) 8/23/2006 10:55:07 PM On Wed, 23 Aug 2006 17:15:17 -0400, Jerry Avins <jya@ieee.org> wrote: >Eric Jacobsen wrote: > >> ... You really only need to sample 2x the >> bandwidth, as Nyquist stated, and in the case of something like a >> square wave one must determine the "bandwidth of interest", i.e., some >> point above which you're not interested or it won't matter. > >C'mon, Eric; I know you know better. Either you sample so fast that >significant aliases are higher than any component of interest (and so >can be filtered digitally later) or you use an anti-alias filter so that >in fact there's nothing to alias. What I had in mind was either that there's natural filtering going on via bandlimiting of the media (even traces on a circuit board are bandlimited), or you've limited your "area of interest" via suitable filtering. Even allowing low-power aliasing into high frequencies is okay if it's outside of the "area of interest" and one is going to take care of it via digital filtering. Pointing out the effects of aliasing would be fundamental in such an article, so I assuming that was assumed. Hmmm...a second order assumption. That must be where I went wrong... ;) >> For sampled-IF (or super-Nyquist as some call it), one must pay >> attention to folding frequencies, etc. > >Calling it "super Nyquist" reveals the ignorance that underlies the problem. As long as it's understood what is meant I don't mind the term. I've not heard it used ambiguously, so I suppose we're stuck with it. I hear it fairly commonly although I do refrain from using it unless present company uses it first...gotta speak the language of the locals. >> It's not hard to sort out, but I think an article like what is >> proposed is always a good thing, if well written, to clarify things >> and help folks avoid the pitfalls. > >Ja! > >Jerry Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org   0 Reply eric.jacobsen (2636) 8/23/2006 10:58:05 PM Jerry Avins wrote: > steve wrote: -- snip -- > > So many misconceptions, so little time. Tim: are you tuned in? > Yes I am, and this discussion is great. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 12:25:45 AM steve wrote: > Jerry Avins wrote: > >>steve wrote: > -- snip -- > > Tim is making many assumptions (unfairly in my opinion) beforehand > about the signal and anti-alias filter in his original post, and then > saying this and that statement is not correct. Mostly I'm assuming that things need to be done in the real world, with real equipment that can be bought for real amounts of money. Given those assumptions I think I'm on track. > Is he assuming frequencies higher then the desired signal exist Yes I am. That's a direct consequence of assuming a real system that is only turned on for a finite period of time. > I think so, but I don't know, is he assuming a non-brick wall > anti-alias filter? Yes I am. That's a direct consequence of assuming that you don't want to wait an infinite amount of time for your filter's output. Falling significantly short of that, I'm staying aware of just how much you have to pay for a filter that's 'practically' brick wall, whatever that means for your particular application. > I think so but who knows. Most other old timers who are pitching in here seem to understand. > Nyquist assumes the ideals, you can't have a theorem otherwise. > That's true. The problem comes about when newbies who have forgotten all of the addenda, exceptions and quid-pro-quos* assume that Nyquist is a design guideline instead of a theoretical limit. * "Alladin", Walt Disney Co., 1992. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 12:34:45 AM Genome wrote: > "Tim Wescott" <tim@seemywebsite.com> wrote in message > news:q6mdnZgxjJhQHnbZnZ2dnUVZ_rGdnZ2d@web-ster.com... > >>Kinda off topic -- >> >>A month or two ago there was a spate of postings on these groups >>displaying a profound misunderstanding of how to apply Nyquist's theorem >>to problems of setting sampling or designing anti-alias filters. I helped >>folks out as much as I could, but it really demands an article, which I am >>currently working on. >> >>The misconceptions that I noticed pretty much boiled down to the following >>two: >> >>One, "I need to monitor a signal that happens at X Hz, so I'm going to >>sample it at 2X Hz". >> >>Two, "I can sample at X Hz, so I'm going to build an anti-alias filter >>with a cutoff of X/2 Hz". >> >>I estimate that answering these misconceptions will only take 3-4k words, >>but I don't want to miss any other big ones. >> >>Have you seen any other real howlers that relate to Nyquist, and what you >>should really be thinking about when you're pondering sampling rates, >>anti-aliasing filters and/or reconstruction filters? >> >>Danke. >> >>-- >> >>Tim Wescott >>Wescott Design Services >>http://www.wescottdesign.com >> > > > I have noticed that for switch mode power supplies the loop crossover > frequency is Fs/2piD and have often modelled such things in spice and they > have behaved themselves where the loop crossover frequency is well above a > half of Fs which rather pisses on Nyquist.... > > What did I miss? > > DNA > > Can you post a link to an example schematic? I don't think you missed anything. First, a switch mode power supply isn't a sampled data system, really. It's certainly time-varying and shares some aspects of a sampled-time system (including the fact that you can use the z transform to improve the accuracy of the analysis if you're a masochist), but it isn't really sampled. Second, while the switching action may alias all sorts of higher-frequency components of the control voltage into the baseband, that doesn't keep the baseband component of the control voltage from being passed through just fine. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 12:45:05 AM 2^n*3^m gives m:n ratio of fft overlap multiply to give correlation as fast mul done by FFT like thing, so i understand? then not FFT infered, possibility! whats up doc?   0 Reply jackokring (1001) 8/24/2006 12:45:06 AM mw wrote: > You should discuss the question of whether it is possible to remove > unwanted aliased-in noise by clever digital filtering in a downstream > calculation. In my understanding this is not possible. But maybe I > slept through that part of the class. No, once it's aliased it's indistinguishable. > > You should discuss what happens to a signal that is filtered and sampled > in one system at rate X, but is transmitted to a receiving system at > update rate Y, then used by that receiving system at rate Z. How should > one select the analog anti-aliasing filter in this situation? > > mw Do you mean where the signal has been resampled at each step? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 12:48:32 AM Paul Burke wrote: > Tim Wescott wrote: > >> >> The misconceptions that I noticed pretty much boiled down to the >> following two: >> >> One, "I need to monitor a signal that happens at X Hz, so I'm going to >> sample it at 2X Hz". >> >> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter >> with a cutoff of X/2 Hz". >> >> I estimate that answering these misconceptions will only take 3-4k >> words, but I don't want to miss any other big ones. > > > Just tell them that they've got to make sure that they sample BELOW the > Nyquist frequency of the HIGHEST frequency present in the signal, and > that the cutoff frequency of a filter isn't the frequency at which the > output is effectively disappeared. Much of the paper is going to be the explanation necessary for me to make just that assertion -- plus explaining what "effectively disappeared" might mean in different systems. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 12:50:01 AM Jerry Avins wrote: > Stef wrote: > >> In comp.arch.embedded, >> mobi <mobien@gmail.com> wrote: >> >>> Do consider this interesting (atleast for me) example >>> >>> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately >>> i start sampling from time = 0. What would i get? Aint i statisifying >>> Nyquist here? >> >> >> No you are not. You seemed to have missed Rune's post in this thread >> about '=' vs ' >'. > > > Equality is enough to avoid aliasing. The inequality is needed to enable > reconstruction. Don't ignore the needed sampling duration in the "almost > equal" case. > > Jerry Or to put it another way: for Fs = (2 + epsilon)F your observation interval is something like 1 t = --------- F*epsilon (more or less -- there's probably a factor of 2 in here that I'm missing). The closer epsilon gets to zero the longer you have to wait. How patient are you? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 12:54:23 AM RRogers wrote: > Tim Wescott wrote: > >>Kinda off topic -- >> >>A month or two ago there was a spate of postings on these groups >>displaying a profound misunderstanding of how to apply Nyquist's theorem >>to problems of setting sampling or designing anti-alias filters. I >>helped folks out as much as I could, but it really demands an article, >>which I am currently working on. >> >>The misconceptions that I noticed pretty much boiled down to the >>following two: >> >>One, "I need to monitor a signal that happens at X Hz, so I'm going to >>sample it at 2X Hz". >> >>Two, "I can sample at X Hz, so I'm going to build an anti-alias filter >>with a cutoff of X/2 Hz". >> >>I estimate that answering these misconceptions will only take 3-4k >>words, but I don't want to miss any other big ones. >> >>Have you seen any other real howlers that relate to Nyquist, and what >>you should really be thinking about when you're pondering sampling >>rates, anti-aliasing filters and/or reconstruction filters? >> >>Danke. >> >>-- >> >>Tim Wescott >>Wescott Design Services >>http://www.wescottdesign.com >> >>Posting from Google? See http://cfaj.freeshell.org/google/ >> >>"Applied Control Theory for Embedded Systems" came out in April. >>See details at http://www.wescottdesign.com/actfes/actfes.html > > More quantitatively, the various questions about anti-alias and > sampling can be answered by reconstructing the signal from the proposed > signal system and them computing the error for antcipated input signals > by taking the difference (in simple systems). Put another way, model > the signal processing path and compare it to what you want, to see if > the approximations you make in your implementation matter. This > provides guidance for sampling rates and anti-aliasing; vesus various > input spectra/signals. In signal processing we typically approximate > perfection (which is sometimes impossible) by various means; the > adequacy depends upon the errors that we allow. Given a description of > what we want and a proposed implementation the errors should be > calculable. Nyquist moerely talks about what can be made to wrk given > perfect resources; reconstruction of an incoming signal of a certain > type. If you feed >2X signals or don't reconstruct/use the data > optimally, you have to do the error analysis to see how much you are > paying for not being perfect. > In other words, you allways have to do an error calculation for an > proposed design and enviroment. > > Ray > > Ray > Bingo. Yes. I'll be making just that point. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 12:56:07 AM jacko wrote: > 2^n*3^m > > gives m:n ratio of fft overlap > > multiply to give correlation > > as fast mul done by FFT like thing, so i understand? > > then not FFT infered, possibility! > > whats up doc? Can english write? maybe (not)   0 Reply jya (12872) 8/24/2006 12:58:33 AM Jonathan Kirwan wrote: > On Wed, 23 Aug 2006 12:13:33 -0400, Phil Hobbs > <pcdh@SpamMeSenseless.pergamos.net> wrote: > > >>Tim Wescott wrote: >> >> >>>Kinda off topic -- >>> >>>A month or two ago there was a spate of postings on these groups >>>displaying a profound misunderstanding of how to apply Nyquist's theorem >>>to problems of setting sampling or designing anti-alias filters. I >>>helped folks out as much as I could, but it really demands an article, >>>which I am currently working on. >>> >>>The misconceptions that I noticed pretty much boiled down to the >>>following two: >>> >>>One, "I need to monitor a signal that happens at X Hz, so I'm going to >>>sample it at 2X Hz". >>> >>>Two, "I can sample at X Hz, so I'm going to build an anti-alias filter >>>with a cutoff of X/2 Hz". >>> >>>I estimate that answering these misconceptions will only take 3-4k >>>words, but I don't want to miss any other big ones. >>> >>>Have you seen any other real howlers that relate to Nyquist, and what >>>you should really be thinking about when you're pondering sampling >>>rates, anti-aliasing filters and/or reconstruction filters? >>> >>>Danke. >> >>The other one I run into is that N. really applies to the bandwidth, not >>the highest frequency as is commonly thought. Harmonic mixers make use >>of this all the time, using the equivalence of the sampled interval to >>the fundamental interval [-f_s/2, f_s/2), and alias down to some lower >>frequency in the process. If you really reconstruct with impulses, you >>can use a bandpass filter to get back the original signal at the >>original carrier frequency. >> >>People also routinely neglect the to account for the zero-order hold in >>their DAC circuits--if you take a signal, run it through an A/D and a >>D/A, you don't wind up with the original signal, but one with an >>additional sinc function rolloff. > > > This last paragraph seems worth emphasizing, particularly on the > subject of sampling rates, as it points out a reason why rather more > than 2.00...01 X sampling may be important. I'm not sure how a > practical reconstruction filter to compensate for ZOH could be > arranged, causal or acausal, otherwise. You need some margin for the > skirts, don't you? > > Jon Actually designing for the sin x / x rolloff isn't too bad as long as you keep your eyes open -- in older digital video systems it was just done with a peaky 2nd-order LC circuit (in newer digital video systems the sampling rate is way higher than the effective resolution of the phosphor, which simplifies things). But you can't avoid the issue of providing sufficiently steep skirts on your filters, both in and out. As you get closer and closer to Nyquist in a 'simple' system your filter complexity goes through the roof, as does the difficulty of actually realizing the filters in analog hardware. This is why many systems that must store or transmit data at close to Nyquist (like music on a CD) have A/D and D/A sample rates that are significantly higher than the internal transmission rate, with digital decimation and interpolation coupled with simplified analog anti-alias and reconstruction filters. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 1:05:48 AM Tim Wescott wrote: > .... snip ... > > Actually designing for the sin x / x rolloff isn't too bad as long as > you keep your eyes open -- in older digital video systems it was just > done with a peaky 2nd-order LC circuit (in newer digital video systems > the sampling rate is way higher than the effective resolution of the > phosphor, which simplifies things). > > But you can't avoid the issue of providing sufficiently steep skirts on > your filters, both in and out. As you get closer and closer to Nyquist > in a 'simple' system your filter complexity goes through the roof, as > does the difficulty of actually realizing the filters in analog > hardware. This is why many systems that must store or transmit data at > close to Nyquist (like music on a CD) have A/D and D/A sample rates that > are significantly higher than the internal transmission rate, with > digital decimation and interpolation coupled with simplified analog > anti-alias and reconstruction filters. IIRC the sin x / x business only applies to sample and hold filtering. The impulse function avoids that. A further point is that the thing that counts in an end to end system, such as telephony, is the net transfer function. You can distribute this in various way with compensating input and output filters. This is generally known as equalization. -- Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net) Available for consulting/temporary embedded and systems. <http://cbfalconer.home.att.net> USE maineline address!   0 Reply cbfalconer (19194) 8/24/2006 2:14:15 AM Somewhere in the Nyquist discussion, you might mention that Nyquist didn't attend MIT or Stafford. He went to a small obscure school in North Dakota. Robert, Did I miss anything? -- Al Clark Danville Signal Processing, Inc. -------------------------------------------------------------------- Purveyors of Fine DSP Hardware and other Cool Stuff Available at http://www.danvillesignal.com   0 Reply dsp825 (454) 8/24/2006 3:05:54 AM FOAD. It was a short, to-the-point comment. The only possible rational argument that can be made to his post is that he didn't trim the quoted text. Tim -- Deep Fryer: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms "CBFalconer" <cbfalconer@yahoo.com> wrote in message news:44EBA509.124CD03F@yahoo.com... > *** top posting fixed *** >> are you going to be including in your artcle cases with filter >> banks, specifically, critical sampled, oversampled etc, and how >> nyquist fits into those implementations? > > Don't top-post. It is rude and contravenes the standard practices > in newsgroups. Your response belongs below, or intermixed with, > the *snipped* material you quote. See the links in my sig. below.   0 Reply tmoranwms2 (39) 8/24/2006 3:11:28 AM "Jim Stewart" <jstewart@jkmicro.com> wrote in message news:UaidnVPZ369OFXbZnZ2dnUVZ_t-dnZ2d@omsoft.com... > I'd guess he wants the word "periodic" in there somewhere (: HIO4? Tim -- Deep Fryer: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms   0 Reply tmoranwms2 (39) 8/24/2006 3:13:42 AM Scott Seidman wrote: > > CommitteeSize = CommitteeSize + 1 ; %!!!!! > > I think what's missing is a demonstration that multiplication with the > Dirac train in time pairs with convolution with the scaled Dirac in > frequency. Without a good figure showing that, the figures under the > "aliasing" subtitle lack some meaning. well, then maybe they should be moved the the "mathematical basis", then. you don't need the convolution with the Dirac comb in the frequency domain thingie if you can show by some other means (i think simpler means) that the spectrum is copied and shifted at all multiples of the sampling frequency. we can show that by showing that the Dirac comb is a periodic function with identical coefficients (all 1 if you scale it right) and then using the frequency shifting theorem. > > As an aside, I'm interested in the analogs in AM. By the book, the > carrier needs to be twice as fast as the highest signal component, but > for Hilbert demodulation, all I can find is the specification that the > signal and carrier not overlap. Is this because the transform > essentially throws out the negative frequencies, so you don't have to > worry about positive/negative overlap? i think so. this kind of AM modulation is called SSB. at least that's what we called it when i was a ham radio kid 38 years ago. > Alternatively, am I just wrong, > and the carrier needs to be twice the highest frequency, even for Hilbert > demod?? duh, i dunno. i think, if you do it the Hilbert way (we didn't have DSP in them olden days of the Heathkit HW100) you can have a carrier frequency of whatever you want. you can separate the positive and negative parts of the original baseband signal and move the positive up or down any amount with the negative part doing the mirror image and moving down or up the opposite amount. r b-j   0 Reply rbj (4087) 8/24/2006 3:34:49 AM Vladimir Vassilevsky wrote: > Recently I run into a problem with the digital PLL occasionally locking > on the aliased frequencies. The problem happens when the signal > constellation has N phase angles. That multiplies the difference phase > by N. Thus the error frequency may appear to be higher then baudrate/2, > causing all kinds of problems. Special care has to be taken to avoid this. I'm not an expert in this area, so maybe you can clarify something. Does the system handle multiple carrier frequencies? If the carrier frequency is fixed, I would expect that the bandwidth of the PLL would be narrow enough to exclude the aliased frequencies. -- Thad   0 Reply ThadSmith (1280) 8/24/2006 4:31:07 AM On 23 Aug 2006 10:39:59 -0700, "steve" <bungalow_steve@yahoo.com> wrote: >Jerry Avins wrote: >> steve wrote: > >> No; it's more than that. It means (among other problems) that there's no >> way to determine the component in phase with the sample clock (sine >> component), so the amplitude remains unknown. >> >sampling at 2.000001X solves that problem, there are no frequencies in >phase with the sample clock anymore, the point I was making > >There is no additional information obtained by sampling at a higher >rate. True, but the "information" on a periodic waveform will be all garnered one helluva lot quicker at 2.1x than at 2.000000001x   0 Reply me4 (19675) 8/24/2006 5:02:21 AM CBFalconer wrote: > Tim Wescott wrote: > > ... snip ... > >>Actually designing for the sin x / x rolloff isn't too bad as long as >>you keep your eyes open -- in older digital video systems it was just >>done with a peaky 2nd-order LC circuit (in newer digital video systems >>the sampling rate is way higher than the effective resolution of the >>phosphor, which simplifies things). >> >>But you can't avoid the issue of providing sufficiently steep skirts on >>your filters, both in and out. As you get closer and closer to Nyquist >>in a 'simple' system your filter complexity goes through the roof, as >>does the difficulty of actually realizing the filters in analog >>hardware. This is why many systems that must store or transmit data at >>close to Nyquist (like music on a CD) have A/D and D/A sample rates that >>are significantly higher than the internal transmission rate, with >>digital decimation and interpolation coupled with simplified analog >>anti-alias and reconstruction filters. > > > IIRC the sin x / x business only applies to sample and hold > filtering. The impulse function avoids that. A further point is > that the thing that counts in an end to end system, such as > telephony, is the net transfer function. You can distribute this > in various way with compensating input and output filters. This is > generally known as equalization. > It applies in spades to zero-order holds on the output, AKA garden-variety DACs. And where aliasing is a problem, there's more to it than the end-to-end transfer function -- strictly speaking you can't formulate a laplace-domain transfer function for a time-varying system, such as a system that incorporates sampled data. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 5:35:21 AM Tim Wescott wrote: > steve wrote: > [...] > >> Nyquist assumes the ideals, you can't have a theorem otherwise. >> > That's true. The problem comes about when newbies who have forgotten > all of the addenda, exceptions and quid-pro-quos* assume that Nyquist is > a design guideline instead of a theoretical limit. The sampling rate is an entirely practical limit in systems which embrace the aliases, rather than trying to eliminate them. In those cases the "practical limit" is not the sampling rate aspect of the sampling theorem, but how well you can approximate the ideal sampler. Steve   0 Reply steveu (1008) 8/24/2006 7:15:11 AM mobi wrote: > Do consider this interesting (atleast for me) example > > Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately > i start sampling from time = 0. What would i get? Aint i statisifying > Nyquist here? > > Regards > > > Tim Wescott wrote: > >>Kinda off topic -- >> >>A month or two ago there was a spate of postings on these groups >>displaying a profound misunderstanding of how to apply Nyquist's theorem >>to problems of setting sampling or designing anti-alias filters. I >>helped folks out as much as I could, but it really demands an article, >>which I am currently working on. >> >>The misconceptions that I noticed pretty much boiled down to the >>following two: >> >>One, "I need to monitor a signal that happens at X Hz, so I'm going to >>sample it at 2X Hz". >> >>Two, "I can sample at X Hz, so I'm going to build an anti-alias filter >>with a cutoff of X/2 Hz". >> >>I estimate that answering these misconceptions will only take 3-4k >>words, but I don't want to miss any other big ones. >> >>Have you seen any other real howlers that relate to Nyquist, and what >>you should really be thinking about when you're pondering sampling >>rates, anti-aliasing filters and/or reconstruction filters? >> >>Danke. >> >>-- >> >>Tim Wescott >>Wescott Design Services >>http://www.wescottdesign.com >> >>Posting from Google? See http://cfaj.freeshell.org/google/ >> >>"Applied Control Theory for Embedded Systems" came out in April. >>See details at http://www.wescottdesign.com/actfes/actfes.html > > Yup! Also try sampling at a constant delay from the sine zero crossing. That is what happens when people blindly follow a "criteria" without knowing the full reason and background.   0 Reply robertbaer (111) 8/24/2006 8:10:36 AM Stef wrote: > In comp.arch.embedded, > mobi <mobien@gmail.com> wrote: > >>Do consider this interesting (atleast for me) example >> >>Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately >>i start sampling from time = 0. What would i get? Aint i statisifying >>Nyquist here? > > > No you are not. You seemed to have missed Rune's post in this thread > about '=' vs ' >'. > > ....then re-state with sampling at 2X+delta where delta is (say) 1Hz!   0 Reply robertbaer (111) 8/24/2006 8:12:14 AM Robert Baer wrote: > Stef wrote: > > > In comp.arch.embedded, > > mobi <mobien@gmail.com> wrote: > > > >>Do consider this interesting (atleast for me) example > >> > >>Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately > >>i start sampling from time = 0. What would i get? Aint i statisifying > >>Nyquist here? > > > > > > No you are not. You seemed to have missed Rune's post in this thread > > about '=' vs ' >'. > > > > > ...then re-state with sampling at 2X+delta where delta is (say) 1Hz! As mentioned earlier, the information rate about a sampled waveform is proportional to the rate above the 2x limit. If you sample at 2.5 the highest frequency iof interest (speaking in a bandwidth sense), you will get sufficient information about said signal faster than if you sample at 2.1x. That obviously impacts the reconstruction filter (as has also been mentioned). I seem to recall (it's been a long time, but makes sense) that the time required to properly train to a reconstructed signal is inversely proportional to the normalised sample rate above the 2x limit. This may seem obvious, but as noted a lot of people don't think through the effect of the sampling or the theory behind it. If I sample at 2.1x, I need more full output cycles at the x rate for full reconstruction than I would need if I sampled at 2.5x. My rule of thumb is to sample at 2.5x at a minimum . There are times I sample at 10x or more. A number of people want a fixed answer for all applications, where there isn't any such panacea. 'It depends' is probably the most common engineering term ;) Something else that might be usefully mentioned in this context is the ADC type used at the input - a Delta Sigma converter inherently decimates the signal, reducing the requirements on the front end anti-aliasing filter. A SAR gives no such assistance. The same consideration of DAC type might also be useful. Cheers PeteS   0 Reply PeterSmith1954 (80) 8/24/2006 10:10:48 AM PeteS wrote: > .... snip ... > > This may seem obvious, but as noted a lot of people don't think > through the effect of the sampling or the theory behind it. If I > sample at 2.1x, I need more full output cycles at the x rate for > full reconstruction than I would need if I sampled at 2.5x. > > My rule of thumb is to sample at 2.5x at a minimum . There are > times I sample at 10x or more. A number of people want a fixed > answer for all applications, where there isn't any such panacea. > 'It depends' is probably the most common engineering term ;) In the PABX telephony example I gave earlier, we initially sampled at 10 kHz to get essentially flat response to 3.5 kHz with constant delay. We upped the sample rate to 12 kHz later to ease the requirements on the filters and equalization. -- Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net) Available for consulting/temporary embedded and systems. <http://cbfalconer.home.att.net> USE maineline address!   0 Reply cbfalconer (19194) 8/24/2006 10:53:08 AM On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com> wrote: >Kinda off topic -- > >A month or two ago there was a spate of postings on these groups >displaying a profound misunderstanding of how to apply Nyquist's theorem >to problems of setting sampling or designing anti-alias filters. I >helped folks out as much as I could, but it really demands an article, >which I am currently working on. > >The misconceptions that I noticed pretty much boiled down to the >following two: > >One, "I need to monitor a signal that happens at X Hz, so I'm going to >sample it at 2X Hz". > >Two, "I can sample at X Hz, so I'm going to build an anti-alias filter >with a cutoff of X/2 Hz". > >I estimate that answering these misconceptions will only take 3-4k >words, but I don't want to miss any other big ones. > >Have you seen any other real howlers that relate to Nyquist, and what >you should really be thinking about when you're pondering sampling >rates, anti-aliasing filters and/or reconstruction filters? > >Danke. >Tim Wescott >Wescott Design Services Hi Tim, Writing about the effects of "periodic sampling" is an interesting and educational thing to do. My guess is that you'll have to address the controversial notion of "negative frequency", as well as why it is valid to show spectral replications (spaced Fs hertz apart) when we draw a freq-domain picture of the spectrum of a discrete (digital) signal. One interesting aspect of periodic sampling is that it's easy to misinterpret the results of software modeling of the process of periodic sampling. That's (I think) what happened when J. L. Smith wrote his "Breaking the Nyquist Barrier" in the July 1995 issue of the IEEE Sig. Processing magazine. I believe Smith misunderstood his software-generated plots when he wrote his embarrassing article. Smith claimed that he could violate the Nyquist Theorem and not lose any information (and avoid any ambiguous information) regarding some time domain signal. Smith's article resulted in a flurry of "Letters To the Editor" that debunked the article (See the Nov. 1995, Jan. 1996, and the May 1996 issues for examples of the letters.) How embarrassing that must have been for both Smith, and the Editors of the magazine who should have known better. Another very "misguided" sampling article was "Apply Fundamentals To Avoid Surprises With Sampled Systems" written by Gerard Fonte and printed in the June 24th 1993 issue of EDN magazine. Fonte also claimed that you could violate Nyquist and not lose any information. Almost every paragraph of that article contains misconceptions and ambiguities regarding the Nyquist sampling theorem. It's truly a "ghastly" article --- and it also caused a deluge of "Letters To the Editor" pointing out all the errors in the article. (See page 25 of the Sept. 30th 1993 issue of the EDN magazine for example.) I thought after all the criticism that Fonte received regarding his 1993 EDN that we'd heard the last from Mr. Fonte. Not so. He wrote another titled "Breaking Nyquist" in the October 1998 issue of the Circuit Cellar magazine. Again he claimed that the Nyquist sampling theorem is not valid and that it can be "broken" without causing "problems". Using vague, ambiguous, undefined terminology, Fonte again claimed that he can tell the difference between an Fo (F sub zero) discrete spectral component of an analog sinewave whose Fo frequency was less than Fs/2 and an Fo discrete spectral component of an aliased analog sinewave whose frequency was greater than Fs/2. In other words, he claims that "aliasing" (violating Nyquist) does NOT cause spectral ambiguity in the frequency domain. I can hardly wait for Fonte's next article. (I'm not being hateful here...Fonte's probably a nice guy whom his family loves.) My guess is, again, Fonte is using software to model the process of periodic sampling, and the signal he is "sampling" is a pure sinewave. Such modeling is very risky in my opinion because it's easy for a beginner in the field of DSP to misinterpret/misunderstand the results of such modeling. Concerning sampling, Bonnie Baker wrote an article titled "Turning Nyquist Upside Down by Undersampling" in the May 12th 2005 issue of EDN magazine. The article discusses bandpass sampling. However, I think the article's title is unfortunate because bandpass sampling does NOT "turn Nyquist upside down" ---bandpass sampling is included in the Nyquist Sampling Theorem. I tell the students in my DSP class that, "Periodic Sampling is one of the most misunderstood topics in DSP." I think I'm justified in making that claim. Hey Tim, I think in any dissertation on "sampling" it would be a good idea to discuss bandpass sampling. Bandpass sampling is not only an interesting topic, but it's a very practical topic in these days of digital communications. (Just my two cents.) See Ya', [-Rick-]   0 Reply R 8/24/2006 11:19:38 AM On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com> wrote: >Kinda off topic -- > >A month or two ago there was a spate of postings on these groups >displaying a profound misunderstanding of how to apply Nyquist's theorem >to problems of setting sampling or designing anti-alias filters. I >helped folks out as much as I could, but it really demands an article, >which I am currently working on. > (snipped) Hi, I just finished posting a long rant about sampling articles written by Gerard Fonte. I just noticed (on the web) that the San Fernando Valley Engineers' Council Inc. has awarded Gerard Fonte an "Outstanding Engineering Achievement Merit Award" for 2006. See: http://engineerscouncil.org/Gallery/EWeekBanquet2006?page=4 [-Rick-]   0 Reply R 8/24/2006 11:50:55 AM Another issue, Isnt it important to always keep into mind what the recustruction filter is? Lets consider this situation. I have an output signal from a ZOH. I want to sample it again and reconstruct it back. Now i think i need only one sample per ZOH symbol. Why? Cos my reconstruction filter can construct my signal exactly from one sample. Certainly i am not satisfying Nyquist in this case. Or maybe i have not been sleeping to well :o) Jerry Avins wrote: > Jonathan Kirwan wrote: > > > ... You need some margin for the skirts, don't you? > > If course, and for other things too. Even if you can be certain that > there is no signal energy above Fmax, you need to sample faster than > 2Fmax in real situations. As it says on traffic a summons in Boston, > "Fail ye not thereof at your peril." > > Jerry > -- > Engineering is the art of making what you want from things you can get. > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF   0 Reply mobien (57) 8/24/2006 11:57:07 AM  Robert Baer wrote: > > mobi wrote: > > > Do consider this interesting (atleast for me) example > > > > Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately > > i start sampling from time = 0. What would i get? Aint i statisifying > > Nyquist here? > > > > > > Yup! > Also try sampling at a constant delay from the sine zero crossing. > That is what happens when people blindly follow a "criteria" without > knowing the full reason and background. What is what happens? Do you actually know what happens if you actually try this in a real world context? Set up a speaker generating the Fs/2 signal. Set up a microphone and and ADC to record the sound at Fs. Are you claiming that you can adjust the sampling phase to produce a digital recording of either full scale or zero? That's what in theory should happen - right? But can you do that in real life? -jim ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----   0 Reply m3740 (420) 8/24/2006 1:02:55 PM Rick Lyons wrote: [...] > Hey Tim, > I think in any dissertation on "sampling" it > would be a good idea to discuss bandpass sampling. > Bandpass sampling is not only an interesting topic, > but it's a very > practical topic in these days of digital > communications. (Just my two cents.) And complex sampling. You must include that, otherwise people won't understand the solid unshakeable reality of negative frequencies. :-) Regards, Steve   0 Reply steveu (1008) 8/24/2006 1:14:42 PM Tim Williams <tmoranwms@charter.net> wrote: > FOAD. It was a short, to-the-point comment. The only possible rational > argument that can be made to his post is that he didn't trim the quoted > text. The only possible rational argument? You really are a complete fucking moron. Tim   0 Reply tim.auton (37) 8/24/2006 1:21:52 PM Rick Lyons wrote: > Hi, > I just finished posting a long rant > about sampling articles written by Gerard Fonte. > > I just noticed (on the web) that the San > Fernando Valley Engineers' Council Inc. > has awarded Gerard Fonte an "Outstanding > Engineering Achievement Merit Award" for 2006. > > See: > http://engineerscouncil.org/Gallery/EWeekBanquet2006?page=4 It has been my experience with local engineers' groups that the people who get awards are the ones who show up regularly.   0 Reply pomerado (75) 8/24/2006 1:34:35 PM jim wrote: > > Robert Baer wrote: >> mobi wrote: >> >>> Do consider this interesting (atleast for me) example >>> >>> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately >>> i start sampling from time = 0. What would i get? Aint i statisifying >>> Nyquist here? >>> >> Yup! >> Also try sampling at a constant delay from the sine zero crossing. >> That is what happens when people blindly follow a "criteria" without >> knowing the full reason and background. > > What is what happens? Do you actually know what happens if you actually > try this in a real world context? Set up a speaker generating the Fs/2 > signal. Set up a microphone and and ADC to record the sound at Fs. Are > you claiming that you can adjust the sampling phase to produce a digital > recording of either full scale or zero? That's what in theory should > happen - right? But can you do that in real life? Of course you can lock the sampler to the sampled waveform or one of its harmonics. Google for "PLL". Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/24/2006 1:40:52 PM mobi wrote: > Another issue, > Isnt it important to always keep into mind what the recustruction > filter is? > > Lets consider this situation. > I have an output signal from a ZOH. I want to sample it again and > reconstruct it back. Now i think i need only one sample per ZOH symbol. > Why? Cos my reconstruction filter can construct my signal exactly from > one sample. Certainly i am not satisfying Nyquist in this case. Or > maybe i have not been sleeping to well :o) > > > Jerry Avins wrote: >> Jonathan Kirwan wrote: >> >>> ... You need some margin for the skirts, don't you? >> If course, and for other things too. Even if you can be certain that >> there is no signal energy above Fmax, you need to sample faster than >> 2Fmax in real situations. As it says on traffic a summons in Boston, >> "Fail ye not thereof at your peril." _______________________________________________________________________ Engineering is the art of making what you want from things you can get. -- Jerry Oh, yes: please don't top post. It makes sequence hard to follow. implications of the sampling theorem needs broadening. pair, or, as in your example, magnitude and derivative. Your view of the cycle. They can be individual samples, they can be a real/quadrature The sampling theorem requires at least two pieces of information per that the derivative is zero at the instant that the sample is taken. case, that its derivative is zero /almost everywhere/. In particular, You are taking advantage of additional knowledge of the signal; in this   0 Reply jya (12872) 8/24/2006 1:55:43 PM Steve Underwood wrote: > Rick Lyons wrote: > [...] >> Hey Tim, >> I think in any dissertation on "sampling" it would be a good idea to >> discuss bandpass sampling. >> Bandpass sampling is not only an interesting topic, but it's a very >> practical topic in these days of digital communications. (Just my two >> cents.) > > And complex sampling. You must include that, otherwise people won't > understand the solid unshakeable reality of negative frequencies. :-) That again? I can show you the trig that explicates "complex" sampling without resort to negative frequencies, but so what? :-) I think a generalization needs to be hammered home. *Any* two independent measurements will do. Value and derivative, for example, as I mentioned by way of explaining why only one sample per cycle is needed to reconstruct the output of a zero-order hold. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/24/2006 2:06:26 PM Rick Lyons wrote: > On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com> > wrote: > -- snip -- > > Hey Tim, > I think in any dissertation on "sampling" it > would be a good idea to discuss bandpass sampling. > Bandpass sampling is not only an interesting topic, > but it's a very > practical topic in these days of digital > communications. (Just my two cents.) > > See Ya', > [-Rick-] > Enough people have mentioned this that I'm going to have to give it serious consideration, but I think I may just point out the existence of bandpass sampling (and complex sampling) then write a follow-on article. I certainly agree with your statement about the sampling process being so often misunderstood. I think this is because sampling seems so simple, yet there is a ton of unintuitive results flowing just below the surface. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/24/2006 2:19:53 PM  Thad Smith wrote: >> Recently I run into a problem with the digital PLL occasionally >> locking on the aliased frequencies. The problem happens when the >> signal constellation has N phase angles. That multiplies the >> difference phase by N. Thus the error frequency may appear to be >> higher then baudrate/2, causing all kinds of problems. Special care >> has to be taken to avoid this. > > > I'm not an expert in this area, so maybe you can clarify something. If the signal constellation has N different phases, then you will have to multiply the phase error by N in order to suppress the influence of the data. The simplest example of that is the squaring Costas loop for BPSK. Any kind of non data-aided PLL will have to do this multiplication of phase. It is typical for modems that the carrier PLL operates once when the current symbol is strobed. Thus if the carrier offset is higher then +/- Baudrate/(2*N), the PLL will not lock properly. > If the carrier > frequency is fixed, I would expect that the bandwidth of the PLL would > be narrow enough to exclude the aliased frequencies. It is not always possible, especially if the carrier is RF and if the incoming SNR is low. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com   0 Reply antispam_bogus (2949) 8/24/2006 2:25:27 PM  Jerry Avins wrote: > > Of course you can lock the sampler to the sampled waveform or one of its > harmonics. Google for "PLL". > I can google PLL, but I wasn't aware that this extra timing circuitry that you are belatedly introducing to the discussion was included in the theory being discussed. Just exactly how does it fit? You already have a switch on the microphone you could just switch it off if you are going to resort to introducing a phony solution - why would you need to go to all the trouble of a PLL? -jim ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----   0 Reply m3740 (420) 8/24/2006 2:30:15 PM jim wrote: > > Jerry Avins wrote: > >> Of course you can lock the sampler to the sampled waveform or one of its >> harmonics. Google for "PLL". >> > > I can google PLL, but I wasn't aware that this extra timing circuitry > that you are belatedly introducing to the discussion was included in the > theory being discussed. Just exactly how does it fit? You already have a > switch on the microphone you could just switch it off if you are going > to resort to introducing a phony solution - why would you need to go to > all the trouble of a PLL? You introduced what you claimed was a practical difficulty of phase lock in the real world into a theoretical discussion about sampling at a fixed phase offset. I pointed out one practical way to overcome the perceived difficulty. If you knew it all along, what was your cavil about? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/24/2006 2:42:00 PM Jerry Avins wrote: > > Of course you can lock the sampler to the sampled waveform or one of its > harmonics. Google for "PLL". Not all signals are periodic waveforms.   0 Reply pomerado (75) 8/24/2006 2:58:09 PM  Jerry Avins wrote: > > You introduced what you claimed was a practical difficulty of phase lock > in the real world into a theoretical discussion about sampling at a > fixed phase offset. I pointed out one practical way to overcome the > perceived difficulty. If you knew it all along, what was your cavil about? I didn't introduce anything. A question of fact was asked "What would happen?" - someone else responded incorrectly - I responded to that response. You snipped all that and now accuse me of introducing the question. If you are going to trigger the sample timing to twice the highest frequency component, then you should have no trouble measuring the amplitude of that frequency component. So apparently you are now saying that those who say you need to sample at more than twice the rate are completely wrong, since there is a practical way to overcome the perceived difficulty. -jim ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----   0 Reply m3740 (420) 8/24/2006 3:10:48 PM "Richard Henry" <pomerado@hotmail.com> wrote in message news:1156426475.306460.133630@75g2000cwc.googlegroups.com... > It has been my experience with local engineers' groups that the people > who get awards are the ones who show up regularly. My mother took a gym class once (this would have been in the early '60s) where something like 20% of the exam score was for putting your name on the paper... she purposely chose to not do as a form of protest. :-) Where I used to work, rumor had it that the main reason a trade rag had just given our device a "widget of the year" award was due to marketing commiting to a high dollar advertising campaign with said trade rag. Hmm... (Those of us in engineering who knew how, uh... lackluster... the widget's performance was knew it could have never won on its technical merits.)   0 Reply JKolstad71HatesSpam (244) 8/24/2006 4:24:08 PM jim wrote: > > Jerry Avins wrote: > >> You introduced what you claimed was a practical difficulty of phase lock >> in the real world into a theoretical discussion about sampling at a >> fixed phase offset. I pointed out one practical way to overcome the >> perceived difficulty. If you knew it all along, what was your cavil about? > > I didn't introduce anything. A question of fact was asked "What would > happen?" - someone else responded incorrectly - I responded to that > response. You snipped all that and now accuse me of introducing the > question. I apparently misunderstood the thrust of your message, quoted in full here: <begin quote> Robert Baer wrote: > > > > mobi wrote: > > >> > > Do consider this interesting (atleast for me) example >> > > >> > > Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately >> > > i start sampling from time = 0. What would i get? Aint i statisifying >> > > Nyquist here? >> > > > > >> > > > > Yup! > > Also try sampling at a constant delay from the sine zero crossing. > > That is what happens when people blindly follow a "criteria" without > > knowing the full reason and background. What is what happens? Do you actually know what happens if you actually try this in a real world context? Set up a speaker generating the Fs/2 signal. Set up a microphone and and ADC to record the sound at Fs. Are you claiming that you can adjust the sampling phase to produce a digital recording of either full scale or zero? That's what in theory should happen - right? But can you do that in real life? -jim <end quote> If you derive the speaker excitation from the ADC clock, there is no difficulty maintaining whatever phase relation you decide upon. What did I not understand? What was the incorrect response you addressed? > If you are going to trigger the sample timing to twice the highest > frequency component, then you should have no trouble measuring the > amplitude of that frequency component. So apparently you are now saying > that those who say you need to sample at more than twice the rate are > completely wrong, since there is a practical way to overcome the > perceived difficulty. I don't get it. What have I written that makes it seem that I believe the amplitude of a component f can be determined by sampling at 2f? We both know it can't be done, and why. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/24/2006 4:40:17 PM Richard Henry wrote: > Jerry Avins wrote: >> Of course you can lock the sampler to the sampled waveform or one of its >> harmonics. Google for "PLL". > > Not all signals are periodic waveforms. We are evidently dealing with a periodic waveform in a discussion of sampling at constant phase. Why drag in a non sequitur? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/24/2006 4:42:59 PM Rick Lyons wrote: .... > I thought after all the criticism that Fonte > received regarding his 1993 EDN that we'd > heard the last from Mr. Fonte. Not so. > He wrote another titled "Breaking Nyquist" > in the October 1998 issue of the Circuit Cellar > magazine. Again he claimed that the > Nyquist sampling theorem is not valid > and that it can be "broken" without > causing "problems". Using vague, ambiguous, > undefined terminology, Fonte again claimed that > he can tell the difference between an Fo > (F sub zero) discrete spectral component of > an analog sinewave whose Fo frequency was less > than Fs/2 and an Fo discrete spectral component > of an aliased analog sinewave whose frequency was > greater than Fs/2. In other words, he claims that > "aliasing" (violating Nyquist) does NOT cause > spectral ambiguity in the frequency domain. > I can hardly wait for Fonte's next article. > > (I'm not being hateful here...Fonte's probably > a nice guy whom his family loves.) > > My guess is, again, Fonte is using software to > model the process of periodic sampling, and the > signal he is "sampling" is a pure sinewave. > Such modeling is very risky in my opinion because > it's easy for a beginner in the field of > DSP to misinterpret/misunderstand the results > of such modeling. > > Concerning sampling, Bonnie Baker wrote an > article titled "Turning Nyquist Upside Down > by Undersampling" in the May 12th 2005 issue > of EDN magazine. The article discusses bandpass > sampling. However, I think the article's > title is unfortunate because bandpass > sampling does NOT "turn Nyquist upside down" > ---bandpass sampling is included in the Nyquist > Sampling Theorem. are any of these online? Rick, i fear that similar stuff is being done in the Wikipedia article. this guy (whose name is very similar to yours and claims to have Alan Oppenheim and Ron Schafer as friends) would say to you that "the converse of the Nyquist-Shannon sampling theorem is not true", meaning that there are cases where frequency components at or above the Nyquist frequence can be validly reconstructed under some circumstances. i think he's talking about bandpass sampling. Anyway, Wikipedia is so selective in the qualifications of editors, i am not sure how this experiment will turn out. sometimes very well written articles get "improved" by some editor that comes in who knows something about the topic (a little bit of knowledge is a dangerous thing) but makes edits that interrupt the flow of concept of the older version. there is no guarantee that the articles will improve in time. sometimes they get worse. r b-j   0 Reply rbj (4087) 8/24/2006 4:52:26 PM  Jerry Avins wrote: > I don't get it. What have I written that makes it seem that I believe > the amplitude of a component f can be determined by sampling at 2f? We > both know it can't be done, and why. It certainly can be done if your sampling points are locked to the signal. As usual your arguments consist of having you cake and eating it too. -jim ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----   0 Reply m3740 (420) 8/24/2006 4:55:38 PM jim wrote: > > Jerry Avins wrote: > >> I don't get it. What have I written that makes it seem that I believe >> the amplitude of a component f can be determined by sampling at 2f? We >> both know it can't be done, and why. > > It certainly can be done if your sampling points are locked to the > signal. As usual your arguments consist of having you cake and eating it It can only be done if the sampling clock is known to be in quadrature with the second harmonic on the signal; the sampling occurs on the peaks. The cases discussed were about sampling at or near the zero crossings. Prior knowledge of the sampling conditions and the signal can lead to systems of equations much simpler than the general cases that were under discussion. Knowing that the samples are taken at the peak od a sine of known frequency allows complete characterization of the signal with a single sample. I don't find such simplifications interesting. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/24/2006 5:12:04 PM  Jerry Avenues wrote: Knowing that the samples are taken at the peak od a sine of > known frequency allows complete characterization of the signal with a > single sample. I don't find such simplifications interesting. So why did you introduce it into the discussion in the first place? ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----   0 Reply m3740 (420) 8/24/2006 5:23:06 PM jim wrote: > > Jerry Avenues wrote: > Knowing that the samples are taken at the peak od a sine of >> known frequency allows complete characterization of the signal with a >> single sample. I don't find such simplifications interesting. > > So why did you introduce it into the discussion in the first place? Because knowing the relative phase of the sampler to the signal's second harmonic is the only condition that makes possible the determination of amplitude when sampling at at 2f, a scenario that you introduced. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/24/2006 5:36:17 PM robert bristow-johnson wrote: > > Rick Lyons wrote: > ... > <snip> >> >> Concerning sampling, Bonnie Baker wrote an >> article titled "Turning Nyquist Upside Down >> by Undersampling" in the May 12th 2005 issue >> of EDN magazine. The article discusses bandpass >> sampling. However, I think the article's >> title is unfortunate because bandpass >> sampling does NOT "turn Nyquist upside down" >> ---bandpass sampling is included in the Nyquist >> Sampling Theorem. > > are any of these online? > > Rick, i fear that similar stuff is being done in the Wikipedia article. > this guy (whose name is very similar to yours and claims to have Alan > Oppenheim and Ron Schafer as friends) would say to you that "the > converse of the Nyquist-Shannon sampling theorem is not true", meaning > that there are cases where frequency components at or above the Nyquist > frequence can be validly reconstructed under some circumstances. i > think he's talking about bandpass sampling. I don't know if he is talking about bandpass sampling. In fact, I have to admit that I'm not even sure of the exact definition of bandpass sampling. However, consider wavelet transform and particularly signals produced by the wavelet synthesis. Such signals have theoretically infinite bandwidth assuming that the scaling function has finite support. This is true also when signals are synthesized only in truncated resolution (i.e. from scale u to v where u and v are finite). It's true even when synthesized in single resolution. Here synthesis means: f(t) = sum_s sum_n x_s[n]*phi_n_s(t), where phi_n_s(t) is the scaling function with translation n and scale s and x_s[n] are the samples from scale (or resolution) s. Even though these signals have infinite bandwidth, they can be sampled and when given the correct scaling function these samples correspond to the original samples used in wavelet synthesis. Here sampling means x_s[n] = <f,phi_n_s>, where f is the analyzed (sampled) function, phi is the scaling function with translation n and scale s. It is obvious that the signal can be later perfectly reconstructed from the samples by wavelet synthesis (assuming the scaling function matched the scaling function used in the original synthesis). In fact, sinc function is just one possible scaling function (in which case one talks about shannon wavelets). This makes traditional sampling just a special case of wavelet transform (in single resolution). Note that the previous comment about infinite bandwidth does not obviously apply to shannon wavelets. Any comments, or corrections? -- Jani Huhtanen Tampere University of Technology, Pori   0 Reply jani.huhtanen (173) 8/24/2006 5:40:30 PM In message <EP8Hg.410$wo2.164@newsfe05.lga>, dated Wed, 23 Aug 2006, Tim
Williams <tmoranwms@charter.net> writes
>"Jim Stewart" <jstewart@jkmicro.com> wrote in message
>news:UaidnVPZ369OFXbZnZ2dnUVZ_t-dnZ2d@omsoft.com...
>> I'd guess he wants the word "periodic" in there somewhere (:
>
>HIO4?
>
Yes, unionised.
--
OOO - Own Opinions Only. Try www.jmwa.demon.co.uk and www.isce.org.uk
2006 is YMMVI- Your mileage may vary immensely.

John Woodgate, J M Woodgate and Associates, Rayleigh, Essex UK

 0
Reply jmw1 (39) 8/24/2006 5:44:42 PM

Tim Wescott wrote:
> Jonathan Kirwan wrote:
>
> > On Wed, 23 Aug 2006 12:13:33 -0400, Phil Hobbs
> > <pcdh@SpamMeSenseless.pergamos.net> wrote:
> >
> >
> >>Tim Wescott wrote:
> >>
> >>
> >>>Kinda off topic --
> >>>
> >>>A month or two ago there was a spate of postings on these groups
> >>>displaying a profound misunderstanding of how to apply Nyquist's theorem
> >>>to problems of setting sampling or designing anti-alias filters.  I
> >>>helped folks out as much as I could, but it really demands an article,
> >>>which I am currently working on.
> >>>
> >>>The misconceptions that I noticed pretty much boiled down to the
> >>>following two:
> >>>
> >>>One, "I need to monitor a signal that happens at X Hz, so I'm going to
> >>>sample it at 2X Hz".
> >>>
> >>>Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> >>>with a cutoff of X/2 Hz".
> >>>
> >>>I estimate that answering these misconceptions will only take 3-4k
> >>>words, but I don't want to miss any other big ones.
> >>>
> >>>Have you seen any other real howlers that relate to Nyquist, and what
> >>>you should really be thinking about when you're pondering sampling
> >>>rates, anti-aliasing filters and/or reconstruction filters?
> >>>
> >>>Danke.
> >>
> >>The other one I run into is that N. really applies to the bandwidth, not
> >>the highest frequency as is commonly thought.  Harmonic mixers make use
> >>of this all the time, using the equivalence of the sampled interval to
> >>the fundamental interval [-f_s/2, f_s/2), and alias down to some lower
> >>frequency in the process.  If you really reconstruct with impulses, you
> >>can use a bandpass filter to get back the original signal at the
> >>original carrier frequency.
> >>
> >>People also routinely neglect the to account for the zero-order hold in
> >>their DAC circuits--if you take a signal, run it through an A/D and a
> >>D/A, you don't wind up with the original signal, but one with an
> >
> >
> > This last paragraph seems worth emphasizing, particularly on the
> > subject of sampling rates, as it points out a reason why rather more
> > than 2.00...01 X sampling may be important.  I'm not sure how a
> > practical reconstruction filter to compensate for ZOH could be
> > arranged, causal or acausal, otherwise.  You need some margin for the
> > skirts, don't you?
> >
> > Jon
> Actually designing for the sin x / x rolloff isn't too bad as long as
> you keep your eyes open -- in older digital video systems it was just
> done with a peaky 2nd-order LC circuit (in newer digital video systems
> the sampling rate is way higher than the effective resolution of the
> phosphor, which simplifies things).
>
> But you can't avoid the issue of providing sufficiently steep skirts on
> your filters, both in and out.  As you get closer and closer to Nyquist
> in a 'simple' system your filter complexity goes through the roof, as
> does the difficulty of actually realizing the filters in analog
> hardware.

I'm not entirely agree with that. There are a lot of analog
antialising filters, which are quite good near the Nyquist. One of them
frequently used is the Cebashev filter (eliptical filter) which design
and implementation is easy up to quite high frequencies
(say 100-200Mhz, at least tested by myself).

greetings,
Vasile


 0
Reply piclist9 (17) 8/24/2006 5:48:41 PM

jim wrote:
> Jerry Avins wrote:
>
> > I don't get it. What have I written that makes it seem that I believe
> > the amplitude of a component f can be determined by sampling at 2f? We
> > both know it can't be done, and why.
>
> It certainly can be done if your sampling points are locked to the
> signal.

works really good when the sampling points are locked to the
zero-crossings of the Nyquist frequency signal.

> As usual your arguments consist of having you cake and eating it too.

(snicker)

sounds to me that expecting a sampler to be phase locked to what we
would normally think is an unknown signal (if it were known, why bother
to sample it to determine its amplitude?) is having one's cake and
eating it too.

r b-j


 0
Reply rbj (4087) 8/24/2006 5:58:53 PM

Jani Huhtanen wrote:
>
> I don't know if he is talking about bandpass sampling. In fact, I have to
> admit that I'm not even sure of the exact definition of bandpass sampling.

*exact* definition, i dunno either (we argue about exact definitions).
but i do know that there are circumstances of a bandpass signal  that
has zero spectrum except for (-f0-B  -f0) and (f0  f0+B) being
sufficiently sampled even when Fs < 2*(f0+B).  i think this is what
"bandpass sampling" refers to.

> However, consider wavelet transform and particularly signals produced by the
> wavelet synthesis. Such signals have theoretically infinite bandwidth
> assuming that the scaling function has finite support. This is true also
> when signals are synthesized only in truncated resolution (i.e. from scale
> u to v where u and v are finite). It's true even when synthesized in single
> resolution. Here synthesis means:
>
>         f(t) = sum_s sum_n x_s[n]*phi_n_s(t), where
>

i'm rewriting this to something that is more visable (monospaced font):

x(t) =  SUM{  SUM{ x_s[n]*phi_s(t-n) }   }
s     n

i have "t" normalized time so it's phi_s(t-n) instead of phi_s(t-nT).

is this a faithful renotation of what you're saying, Jani?

> phi_s(t-n) is the scaling function with translation n and scale s and x_s[n]
> are the samples from scale (or resolution) s.
>
> Even though these signals have infinite bandwidth, they can be sampled and
> when given the correct scaling function these samples correspond to the
> original samples used in wavelet synthesis. Here sampling means

x_s[n] = <x(t),phi_s(t-n)>,

> where x(t) is the analyzed (sampled) function, phi_s(t-n) is the scaling function with
> translation n and scale s. It is obvious that the signal can be later
> perfectly reconstructed from the samples by wavelet synthesis (assuming the
> scaling function matched the scaling function used in the original
> synthesis).
>
> In fact, sinc function is just one possible scaling function (in which case
> one talks about shannon wavelets).

yeah, but those guys are all bandlimited and there need be only one
scaling factor so there is no SUM_s above, only the SUM_n

> This makes traditional sampling just a
> special case of wavelet transform (in single resolution). Note that the
> previous comment about infinite bandwidth does not obviously apply to
> shannon wavelets.

i guess i did notice.

the only thing i would say is that it's about the wavelet transform and
is not about the Nyquist-Shannon sampling and reconstruction theorem.

r b-j


 0
Reply rbj (4087) 8/24/2006 6:18:30 PM

robert bristow-johnson wrote:

> Jani Huhtanen wrote:
>>
>> I don't know if he is talking about bandpass sampling. In fact, I have to
>> admit that I'm not even sure of the exact definition of bandpass
>> sampling.
>
> *exact* definition, i dunno either (we argue about exact definitions).
> but i do know that there are circumstances of a bandpass signal  that
> has zero spectrum except for (-f0-B  -f0) and (f0  f0+B) being
> sufficiently sampled even when Fs < 2*(f0+B).  i think this is what
> "bandpass sampling" refers to.
>
>> However, consider wavelet transform and particularly signals produced by
>> the wavelet synthesis. Such signals have theoretically infinite bandwidth
>> assuming that the scaling function has finite support. This is true also
>> when signals are synthesized only in truncated resolution (i.e. from
>> scale u to v where u and v are finite). It's true even when synthesized
>> in single resolution. Here synthesis means:
>>
>>         f(t) = sum_s sum_n x_s[n]*phi_n_s(t), where
>>
>
> i'm rewriting this to something that is more visable (monospaced font):
>
>
>       x(t) =  SUM{  SUM{ x_s[n]*phi_s(t-n) }   }
>                s     n
>
> i have "t" normalized time so it's phi_s(t-n) instead of phi_s(t-nT).
>
> is this a faithful renotation of what you're saying, Jani?

Yep.

>
>> phi_s(t-n) is the scaling function with translation n and scale s and
>> x_s[n] are the samples from scale (or resolution) s.
>>
>> Even though these signals have infinite bandwidth, they can be sampled
>> and when given the correct scaling function these samples correspond to
>> the original samples used in wavelet synthesis. Here sampling means
>
>          x_s[n] = <x(t),phi_s(t-n)>,
>
>> where x(t) is the analyzed (sampled) function, phi_s(t-n) is the scaling
>> function with translation n and scale s. It is obvious that the signal
>> can be later perfectly reconstructed from the samples by wavelet
>> synthesis (assuming the scaling function matched the scaling function
>> used in the original synthesis).
>>
>> In fact, sinc function is just one possible scaling function (in which
>> case one talks about shannon wavelets).
>
> yeah, but those guys are all bandlimited and there need be only one
> scaling factor so there is no SUM_s above, only the SUM_n

See below.

>
>> This makes traditional sampling just a
>> special case of wavelet transform (in single resolution). Note that the
>> previous comment about infinite bandwidth does not obviously apply to
>> shannon wavelets.
>
> i guess i did notice.
>
>
> the only thing i would say is that it's about the wavelet transform and
> is not about the Nyquist-Shannon sampling and reconstruction theorem.

OK, consider

f(t) = SUM_n x[n]*phi(t-n)  (1)
x[n] = <f(t), phi(t-n)>     (2)

Do we agree that if phi(t) = sinc(t), then (2) equals to Nyquist-Shannon
sampling of bandlimited signal and (1) to reconstruction of the said
signal? In a way the dirac-comb and anti-aliasing filter are combined into
(2).

Now consider
{ 1, when 0 < t < 1
phi(t) = {
{ 0, otherwise

which corresponds to the scaling function of the simplest possible wavelet
trasform: Haar transform. In this case, (1) corresponds to synthesis
(reconstruction) at scale 0 and (2) corresponds to analysis (sampling) at
scale 0. Again, as I previously stated, if f(t) is synthesized by (1) it
can be sampled by (2) and subsequently perfectly reconstructed by (1).

What I'm getting at is that, there is no need for SUM_s in the case of
wavelet transform either, but _only_ if the analyzed signal is synthesized
in single resolution. Surely you see that both, Nyquist-Shannon and Haar
seem very alike? Difference is in the requirements for f(t). In case of
Nyquist-Shannon, f(t) has to be bandlimited (sinc) and in case of Haar,
f(t) has to be piecewise constant.

So perhaps this guy, talking about the converse of the Nyquist-Shannon
sampling theorem not being true, was referring to something similar I
described? Or did I competely misread you?

--
Jani Huhtanen
Tampere University of Technology, Pori

 0
Reply jani.huhtanen (173) 8/24/2006 7:00:31 PM

Jani Huhtanen wrote:
>
> So perhaps this guy, talking about the converse of the Nyquist-Shannon
> sampling theorem not being true, was referring to something similar I
> described?

i doubt it.  i think he was talking about "bandpass sampling".

> Or did I competely misread you?

not me.  i think you and i have completely coherent communication.  i
wavelet transform thing but about cases where Fs < 2(f0+B) (the highest
frequency) and someone (using bandpass sampling) they are still able to
reconstruct.

r b-j


 0
Reply rbj (4087) 8/24/2006 8:05:56 PM

vasile wrote:
> Tim Wescott wrote:
>
.... snip ...
>>
>> But you can't avoid the issue of providing sufficiently steep
>> skirts on your filters, both in and out.  As you get closer and
>> closer to Nyquist in a 'simple' system your filter complexity
>> goes through the roof, as does the difficulty of actually
>> realizing the filters in analog hardware.
>
>   I'm not entirely agree with that. There are a lot of analog
> antialising filters, which are quite good near the Nyquist. One
> of them frequently used is the Cebashev filter (eliptical
> filter) which design and implementation is easy up to quite
> high frequencies (say 100-200Mhz, at least tested by myself).

That's fine if you don't care about phase linearity (time delay).
Chebychev filters are notoriously poor at preserving phase, or
having constant delay characteristics.  This results in heavy
distortion of analog waveforms, and will manifest itself as such
effects as overshoot and ringing.  A Bessel filter is designed to
minimize this effect, but has much more gentle rejection slopes.

--
Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net)
Available for consulting/temporary embedded and systems.


 0
Reply cbfalconer (19194) 8/24/2006 9:11:26 PM


robert bristow-johnson wrote:

> sounds to me that expecting a sampler to be phase locked to what we
> would normally think is an unknown signal (if it were known, why bother
> to sample it to determine its amplitude?) is having one's cake and
> eating it too.

Is there an echo in here. The above is exactly what I just said.

The question was asked - What really happens when you sample a frequency
at Fs/2.

Set up a speaker generating the Fs/2 signal. Set up a microphone and
ADC to sample the sound at Fs. What really happens?  If you adjust the
phase of the sampling can you record silence? This was not a theoretical
question. We all know how it should work in a perfect world. How does it
work in the real world?

No locking the ADC to the signal allowed since that would be a
completely different question that no one asked and no one is interested
in.

-jim

----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==----
http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups
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 0
Reply m3740 (420) 8/24/2006 9:37:50 PM

Jerry Avins wrote:
> jim wrote:
> >
> > Robert Baer wrote:
> >> mobi wrote:
> >>
> >>> Do consider this interesting (atleast for me) example
> >>>
> >>> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
> >>> i start sampling from time = 0. What would i get? Aint i statisifying
> >>> Nyquist here?
> >>>
> >>    Yup!
> >>    Also try sampling at a constant delay from the sine zero crossing.
> >>    That is what happens when people blindly follow a "criteria" without
> >> knowing the full reason and background.
> >
> > What is what happens? Do you actually know what happens if you actually
> > try this in a real world context? Set up a speaker generating the Fs/2
> > signal. Set up a microphone and and ADC to record the sound at Fs. Are
> > you claiming that you can adjust the sampling phase to produce a digital
> > recording of either full scale or zero? That's what in theory should
> > happen - right? But can you do that in real life?
>
> Of course you can lock the sampler to the sampled waveform or one of its

However the phase information fed to the PLL to allow it to lock
would constitute additional samples, thus raising the total sample
rate of all information coming into the system above Fs/2.  You
have to count all the samples, not just the ones you label as
"samples".

IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M


 0
Reply rhnlogic (1111) 8/24/2006 11:30:24 PM

Ron N. wrote:
> Jerry Avins wrote:
>> jim wrote:
>>> Robert Baer wrote:
>>>> mobi wrote:
>>>>
>>>>> Do consider this interesting (atleast for me) example
>>>>>
>>>>> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
>>>>> i start sampling from time = 0. What would i get? Aint i statisifying
>>>>> Nyquist here?
>>>>>
>>>>    Yup!
>>>>    Also try sampling at a constant delay from the sine zero crossing.
>>>>    That is what happens when people blindly follow a "criteria" without
>>>> knowing the full reason and background.
>>> What is what happens? Do you actually know what happens if you actually
>>> try this in a real world context? Set up a speaker generating the Fs/2
>>> signal. Set up a microphone and and ADC to record the sound at Fs. Are
>>> you claiming that you can adjust the sampling phase to produce a digital
>>> recording of either full scale or zero? That's what in theory should
>>> happen - right? But can you do that in real life?
>> Of course you can lock the sampler to the sampled waveform or one of its
>
> However the phase information fed to the PLL to allow it to lock
> would constitute additional samples, thus raising the total sample
> rate of all information coming into the system above Fs/2.  You
> have to count all the samples, not just the ones you label as
> "samples".

That's an interesting assertion. Can you justify it?

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/24/2006 11:54:46 PM

Jerry Avins wrote:

> The Nyquist criterion does indeed assume ideal conditions.

The Nyquist criterion tells you if your closed-loop feedback system
will be stable or not.  It has nothing to do with sampling.

-a


 0
Reply Bassman59a (39) 8/24/2006 11:59:19 PM

Andy Peters wrote:
> Jerry Avins wrote:
>
>
>>The Nyquist criterion does indeed assume ideal conditions.
>
>
> The Nyquist criterion tells you if your closed-loop feedback system
> will be stable or not.  It has nothing to do with sampling.
>
> -a
>
You're thinking of the Barkhausen criterion, which gives a necessary,
but not sufficient, condition for oscillation.  While it's useful for
stable or not -- and having built plenty of type III control systems I
can assure you that 180 degrees of phase shift and gain >> 1 doesn't
mean you're oscillating.

The Nyquist rate is about sampling, and while I haven't heard it called
a "criterion", it's still about sampling.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 0
Reply tim177 (4434) 8/25/2006 12:20:10 AM

jim wrote:

>
> robert bristow-johnson wrote:
>
>
>>sounds to me that expecting a sampler to be phase locked to what we
>>would normally think is an unknown signal (if it were known, why bother
>>to sample it to determine its amplitude?) is having one's cake and
>>eating it too.
>
>
> Is there an echo in here. The above is exactly what I just said.
>
> The question was asked - What really happens when you sample a frequency
> at Fs/2.
>
> 	Set up a speaker generating the Fs/2 signal. Set up a microphone and
> ADC to sample the sound at Fs. What really happens?  If you adjust the
> phase of the sampling can you record silence? This was not a theoretical
> question. We all know how it should work in a perfect world. How does it
> work in the real world?
>
What really happens is that you get a signal at Fs/2 that is sometimes
big and sometimes small, and you have no clue if it's _actually_ a
signal at Fs/2 that's sometimes big and sometimes small, or a signal
that's big and sometimes at Fs/2 and sometimes slightly off.

Which is why you don't want to do it.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 0
Reply tim177 (4434) 8/25/2006 12:39:29 AM

Jani Huhtanen wrote:

> robert bristow-johnson wrote:
>
>
>
> I don't know if he is talking about bandpass sampling. In fact, I have to
> admit that I'm not even sure of the exact definition of bandpass sampling.
>
> However, consider wavelet transform and particularly signals produced by the
> wavelet synthesis. Such signals have theoretically infinite bandwidth
> assuming that the scaling function has finite support. This is true also
> when signals are synthesized only in truncated resolution (i.e. from scale
> u to v where u and v are finite). It's true even when synthesized in single
> resolution. Here synthesis means:
>
>         f(t) = sum_s sum_n x_s[n]*phi_n_s(t), where
>
> phi_n_s(t) is the scaling function with translation n and scale s and x_s[n]
> are the samples from scale (or resolution) s.
>
> Even though these signals have infinite bandwidth, they can be sampled and
> when given the correct scaling function these samples correspond to the
> original samples used in wavelet synthesis. Here sampling means
>
>         x_s[n] = <f,phi_n_s>,
>
> where f is the analyzed (sampled) function, phi is the scaling function with
> translation n and scale s. It is obvious that the signal can be later
> perfectly reconstructed from the samples by wavelet synthesis (assuming the
> scaling function matched the scaling function used in the original
> synthesis).
>
> In fact, sinc function is just one possible scaling function (in which case
> one talks about shannon wavelets). This makes traditional sampling just a
> special case of wavelet transform (in single resolution). Note that the
> previous comment about infinite bandwidth does not obviously apply to
> shannon wavelets.
>
>
I'm not a wavelet guru, but if I'm reading your math right you are
constraining yourself to sampling a finite number of wavelets, each of
which may have frequency content going out to infinity, and being able
to perfectly reconstruct the signal.

I'll believe you that this is true*.

Where your observation falls down, however, is that there are no
perfect, physically realizable 'wavelet filters' to use -- you can
_synthesize_ a function in some mathematical domain, but you can't go to
and from physical reality with arbitrary wavelets.

I suspect that even if you could make some magic wavelet filter bank
with a finite number of wavelets that you would have to constrain your
signal to be composed only of the wavelets in your set, and any
additional wavelets in the actual signal would 'alias' into your set of
realized wavelets**.

* Gee, my syntax is really fractured this evening.

** Really, really fractured.  I think it's the subject matter, but maybe
it's just been a long day.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 0
Reply tim177 (4434) 8/25/2006 12:50:12 AM

Andy Peters wrote:
> Jerry Avins wrote:
>
>> The Nyquist criterion does indeed assume ideal conditions.
>
> The Nyquist criterion tells you if your closed-loop feedback system
> will be stable or not.  It has nothing to do with sampling.

The Nyquist sampling theorem. We weren't carrying on about enclosing the
point -1, 0 on a Nyquist plot in the s plane. That guy Nyquist had more
than one feather in his cap. Spirule, anyone?

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/25/2006 1:00:23 AM

Tim Wescott wrote:
> Andy Peters wrote:
>> Jerry Avins wrote:
>>
>>
>>> The Nyquist criterion does indeed assume ideal conditions.
>>
>>
>> The Nyquist criterion tells you if your closed-loop feedback system
>> will be stable or not.  It has nothing to do with sampling.
>>
>> -a
>>
> You're thinking of the Barkhausen criterion, which gives a necessary,
> but not sufficient, condition for oscillation.  While it's useful for
> stable or not -- and having built plenty of type III control systems I
> can assure you that 180 degrees of phase shift and gain >> 1 doesn't
> mean you're oscillating.
>
> The Nyquist rate is about sampling, and while I haven't heard it called
> a "criterion", it's still about sampling.

But see http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node43.html
http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node45.html and
http://www.facstaff.bucknell.edu/mastascu/eControlHTML/Freq/Nyquist2.html

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

 0
Reply jya (12872) 8/25/2006 1:04:26 AM

CBFalconer wrote:
> vasile wrote:
>> Tim Wescott wrote:
>>
> ... snip ...
>>> But you can't avoid the issue of providing sufficiently steep
>>> skirts on your filters, both in and out.  As you get closer and
>>> closer to Nyquist in a 'simple' system your filter complexity
>>> goes through the roof, as does the difficulty of actually
>>> realizing the filters in analog hardware.
>>   I'm not entirely agree with that. There are a lot of analog
>> antialising filters, which are quite good near the Nyquist. One
>> of them frequently used is the Cebashev filter (eliptical
>> filter) which design and implementation is easy up to quite
>> high frequencies (say 100-200Mhz, at least tested by myself).
>
> That's fine if you don't care about phase linearity (time delay).
> Chebychev filters are notoriously poor at preserving phase, or
> having constant delay characteristics.  This results in heavy
> distortion of analog waveforms, and will manifest itself as such
> effects as overshoot and ringing.  A Bessel filter is designed to
> minimize this effect, but has much more gentle rejection slopes.
>
I wonder if he really means Chebyshev or elliptic (Cauer)? They both
ring badly, but the Cauer rings like a bell if you design one for any
reasonably steep cutoff slope. In a particular application you might not
anti-aliasing qualities of the filter, since it can allow bursts of out
of band energy through.

Steve

 0
Reply steveu (1008) 8/25/2006 2:09:44 AM

Oli Filth wrote:
> David Ashley said the following on 23/08/2006 19:28:
>> I don't think Wikipedia's going away. I find myself using it more and
>> more as a first step to getting any info on some new subject -- even
>
> In some areas, Wikipedia is great, in others it's dire (no disrepect
> intended to anyone that contributes, myself included).  Articles about
> comms and signal processing (as relevant examples) are on the whole
> scant, badly written and error-prone.  However, I'm sure this will
> change over time.

Do you think it will change for the better or the worse? It seems
numerous articles on Wikipedia start out pretty good, but editors much
less knowledgeable than the original author gradually scramble them.

>> Now here's a thought -- if Wikipedia can become financially
>> viable in its own right (currently it depends on donations) maybe a
>> business model can appear where based on number of "views" of
>> pages, the contributing authors can get some $sent their >> way. >> >> Yes -- it's viable! >> >> #1) Suggest the possibility >> #2) ??? >> #3) Profit! > > Nice idea, but I don't think it's ever going to happen. For one, the > Wikipedia administrators are already working hard to reduce the > systematic bias that exists in Wikipedia (see > http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Countering_systemic_bias), > introducing a financial incentive to writing good articles could only > make this worse. Why would that be? If people are paid to do a good job writing articles, they might possibly do so. Right now, any financial or other personal gain from contributing lies outside Wikipedia, leading to blatant agendas in the writing. I think giving prominence to the names of valued authors might be a solid incentive to good work. Someone pointed me to the Wikipedia articles on a couple of porn stars. From there you can link to many others. They seem to have been written with a genuine affection and interest for the subject matter. I was amazed to see how much effort people will put into that. If they could only encourage a similar level of dedication in the technical articles Wikipedia could become outstanding. :-) Steve   0 Reply steveu (1008) 8/25/2006 2:19:22 AM  Tim Wescott wrote: > > > What really happens is that you get a signal at Fs/2 that is sometimes > big and sometimes small, and you have no clue if it's _actually_ a > signal at Fs/2 that's sometimes big and sometimes small, or a signal > that's big and sometimes at Fs/2 and sometimes slightly off. OK. > > Which is a bad thing. Maybe. There are situations where it doesn't matter if its a fluctuation in the amplitude or frequency. Like a 44khz sound recording where your ears can't discern the difference anyway. Bad or good always depends on what you are attempting to accomplish. I never said it was a good thing or a bad thing. What I did say was sampling a sine wave at Fs/2 mo matter what you think the phase is produces a good indication of how non-linear and inaccurate your signal and sampling system really are. -jim > > Which is why you don't want to do it. > > -- > > Tim Wescott > Wescott Design Services > http://www.wescottdesign.com > > Posting from Google? See http://cfaj.freeshell.org/google/ > > "Applied Control Theory for Embedded Systems" came out in April. > See details at http://www.wescottdesign.com/actfes/actfes.html ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----   0 Reply m3740 (420) 8/25/2006 2:42:23 AM >> You should discuss what happens to a signal that is filtered and >> sampled in one system at rate X, but is transmitted to a receiving >> system at update rate Y, then used by that receiving system at rate >> Z. How should one select the analog anti-aliasing filter in this >> situation? >> >> mw > > Do you mean where the signal has been resampled at each step? > No, not re-sampled (from analog to digital) by each system, but instead sent digitally to the next system such that the receiving system only uses some of the data, not every sample. Let's say the initial ADC step has a 1000 samples/sec conversion rate, then the signal is broadcast out, and a receiver system receives at a rate of 200 samples/sec. Then the processing inside that system only has time to perform 50 calculations/sec. Would the analog anti-aliasing filter selection be dependent on the 50 calc/sec? If that's true you'd have to select the aliasing filter based on the slowest end user of the data. It seems odd that if you design an ADC stage, you'd have to choose analog filtering based on the slowest performing "weakest link" in the eventual design. Opinions?   0 Reply mw9936 (11) 8/25/2006 3:14:44 AM mw wrote: >>> You should discuss what happens to a signal that is filtered and >>> sampled in one system at rate X, but is transmitted to a receiving >>> system at update rate Y, then used by that receiving system at rate >>> Z. How should one select the analog anti-aliasing filter in this >>> situation? >>> >>> mw >> >> Do you mean where the signal has been resampled at each step? >> > No, not re-sampled (from analog to digital) by each system, but instead > sent digitally to the next system such that the receiving system only > uses some of the data, not every sample. Let's say the initial ADC step > has a 1000 samples/sec conversion rate, then the signal is broadcast > out, and a receiver system receives at a rate of 200 samples/sec. Then > the processing inside that system only has time to perform 50 > calculations/sec. > > Would the analog anti-aliasing filter selection be dependent on the 50 > calc/sec? If that's true you'd have to select the aliasing filter based > on the slowest end user of the data. It seems odd that if you design an > ADC stage, you'd have to choose analog filtering based on the slowest > performing "weakest link" in the eventual design. Opinions? It's not a matter of opinion; this is well charted territory. Look up interpolation and decimation, or up- and down converting. Digital filtering is usually required at each stage. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/25/2006 3:32:09 AM jim wrote: > robert bristow-johnson wrote: > > > sounds to me that expecting a sampler to be phase locked to what we > > would normally think is an unknown signal (if it were known, why bother > > to sample it to determine its amplitude?) is having one's cake and > > eating it too. > > Is there an echo in here. The above is exactly what I just said. well, you said this: > > What is what happens? Do you actually know what happens if you actually > try this in a real world context? Set up a speaker generating the Fs/2 > signal. Set up a microphone and and ADC to record the sound at Fs. Are > you claiming that you can adjust the sampling phase to produce a digital > recording of either full scale or zero? That's what in theory should > happen - right? But can you do that in real life? > and you said this: > > If you are going to trigger the sample timing to twice the highest > frequency component, then you should have no trouble measuring the > amplitude of that frequency component. i didn't realize you were being facetious here. > So apparently you are now saying > that those who say you need to sample at more than twice the rate are > completely wrong, since there is a practical way to overcome the > perceived difficulty. .... > The question was asked - What really happens when you sample a frequency > at Fs/2. we know what happens when you sample something at precisely Nyquist. it only matters what relative phase the sampling is done on and the rest is unremarkable. there is nothing else that happens. r b-j   0 Reply rbj (4087) 8/25/2006 3:39:40 AM Jerry Avins wrote: > Tim Wescott wrote: > >> Andy Peters wrote: >> >>> Jerry Avins wrote: >>> >>> >>>> The Nyquist criterion does indeed assume ideal conditions. >>> >>> >>> >>> The Nyquist criterion tells you if your closed-loop feedback system >>> will be stable or not. It has nothing to do with sampling. >>> >>> -a >>> >> You're thinking of the Barkhausen criterion, which gives a necessary, >> but not sufficient, condition for oscillation. While it's useful for >> building oscillators, it doesn't help you tell if your control system >> is stable or not -- and having built plenty of type III control >> systems I can assure you that 180 degrees of phase shift and gain >> 1 >> doesn't mean you're oscillating. >> >> The Nyquist rate is about sampling, and while I haven't heard it >> called a "criterion", it's still about sampling. > > > But see http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node43.html > http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node45.html and > http://www.facstaff.bucknell.edu/mastascu/eControlHTML/Freq/Nyquist2.html > > Jerry Y'know, I use that all the time, but I totally forgot it's name. Whadda ya know. AFAIK Nyquist got his first fame with the analysis of negative feedback in vacuum tube amplifiers back in the '20s when it was all magic. _Then_ he got into cahoots with Shannon to make his rate. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/25/2006 4:42:31 AM mw wrote: >>> You should discuss what happens to a signal that is filtered and >>> sampled in one system at rate X, but is transmitted to a receiving >>> system at update rate Y, then used by that receiving system at rate >>> Z. How should one select the analog anti-aliasing filter in this >>> situation? >>> >>> mw >> >> >> Do you mean where the signal has been resampled at each step? >> > No, not re-sampled (from analog to digital) by each system, but instead > sent digitally to the next system such that the receiving system only > uses some of the data, not every sample. Let's say the initial ADC step > has a 1000 samples/sec conversion rate, then the signal is broadcast > out, and a receiver system receives at a rate of 200 samples/sec. Then > the processing inside that system only has time to perform 50 > calculations/sec. When I said 'resampling' I meant precisely the step where you go from 1000 samp/sec to 200 samp/sec, and again going down to 50 samp/sec. > > Would the analog anti-aliasing filter selection be dependent on the 50 > calc/sec? If that's true you'd have to select the aliasing filter based > on the slowest end user of the data. It seems odd that if you design an > ADC stage, you'd have to choose analog filtering based on the slowest > performing "weakest link" in the eventual design. Opinions? > In my opinion that would be a pretty odd system. Without opinion, if you interpolate correctly before you decimate then no, you wouldn't have to take that end-use 50 sample/sec into account at the initial stage. If you don't, you do. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/25/2006 4:46:48 AM In article <44ED0B77.96688D06@yahoo.com>, cbfalconer@yahoo.com says... > IIRC the sin x / x business only applies to sample and hold > filtering. The impulse function avoids that. A further point is > that the thing that counts in an end to end system, such as > telephony, is the net transfer function. You can distribute this > in various way with compensating input and output filters. This is > generally known as equalization. Just jumping in here for a second (and I'm not sure if this is being debated or not) but I thought the second part of Nyquist is, to reconstruct your samples you pass them through an ideal low-pass filter. The ideal low-pass has the impulse response of sin(x)/x aka sinc(x) and as you pass your impulses through it, the filter "perfectly" interpolates the data between the input impulses. This works as long as you satisfy the sampling rate (whatever that is) and your low-pass has infinite roll-off. Obviously real world re-construction filters do not have that... John.   0 Reply bogus4011 (7) 8/25/2006 4:55:31 AM John wrote: > In article <44ED0B77.96688D06@yahoo.com>, cbfalconer@yahoo.com says... > > >>IIRC the sin x / x business only applies to sample and hold >>filtering. The impulse function avoids that. A further point is >>that the thing that counts in an end to end system, such as >>telephony, is the net transfer function. You can distribute this >>in various way with compensating input and output filters. This is >>generally known as equalization. > > > Just jumping in here for a second (and I'm not sure if this is being > debated or not) but I thought the second part of Nyquist is, to > reconstruct your samples you pass them through an ideal low-pass filter. > Correct. > The ideal low-pass has the impulse response of sin(x)/x aka sinc(x) and > as you pass your impulses through it, the filter "perfectly" > interpolates the data between the input impulses. This works as long as > you satisfy the sampling rate (whatever that is) and your low-pass has > infinite roll-off. Yes. > > Obviously real world re-construction filters do not have that... Correct. In fact, any filter that has a frequency response that goes to zero and stays there must have an impulse response that extends infinitely into both positive and negative time. This means that a real-world version of that filter will have to have infinite delay, which is kind of hard to implement (but easy to fake -- "Well boss, you said 'perfect' filtering, so we're just waiting for the response to be non-zero here. Don't hold your breath."). -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/25/2006 5:24:57 AM jim wrote: > Jerry Avins wrote: > > > I don't get it. What have I written that makes it seem that I believe > > the amplitude of a component f can be determined by sampling at 2f? We > > both know it can't be done, and why. > > It certainly can be done if your sampling points are locked to the > signal. As usual your arguments consist of having you cake and eating it > too. How do you lock your sampling points to the signal with taking additional samples (or equivalent information or measurements)? The scope trigger is, in fact, an additional measurement, thus giving you a total sample rate higher than Fs (as in total measurements per second) when the trigger is enabled. With the trigger off, how would you know if your sampling points were locked or not? IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M   0 Reply rhnlogic (1111) 8/25/2006 5:46:47 AM Tim Wescott wrote: > mw wrote: > .... snip ... > > When I said 'resampling' I meant precisely the step where you go from > 1000 samp/sec to 200 samp/sec, and again going down to 50 samp/sec. >> >> Would the analog anti-aliasing filter selection be dependent on the >> 50 calc/sec? If that's true you'd have to select the aliasing >> filter based on the slowest end user of the data. It seems odd >> that if you design an ADC stage, you'd have to choose analog >> filtering based on the slowest performing "weakest link" in the >> eventual design. Opinions? > > In my opinion that would be a pretty odd system. > > Without opinion, if you interpolate correctly before you decimate > then no, you wouldn't have to take that end-use 50 sample/sec into > account at the initial stage. If you don't, you do. Think about it. If you drop 4 out of 5 samples to get tothe 200 samp/sec, what is the difference (to the receiver) from original sampling at 200/sec. You have to consider the overall system. -- Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net) Available for consulting/temporary embedded and systems. <http://cbfalconer.home.att.net> USE maineline address!   0 Reply cbfalconer (19194) 8/25/2006 6:06:46 AM Tim Wescott wrote: > Jani Huhtanen wrote: > >> robert bristow-johnson wrote: >> > -- comments about bandpass sampling snipped -- >> >> >> I don't know if he is talking about bandpass sampling. In fact, I have to >> admit that I'm not even sure of the exact definition of bandpass >> sampling. >> >> However, consider wavelet transform and particularly signals produced by >> the wavelet synthesis. Such signals have theoretically infinite bandwidth >> assuming that the scaling function has finite support. This is true also >> when signals are synthesized only in truncated resolution (i.e. from >> scale u to v where u and v are finite). It's true even when synthesized >> in single resolution. Here synthesis means: >> >> f(t) = sum_s sum_n x_s[n]*phi_n_s(t) (1) , where >> >> phi_n_s(t) is the scaling function with translation n and scale s and >> x_s[n] are the samples from scale (or resolution) s. >> >> Even though these signals have infinite bandwidth, they can be sampled >> and when given the correct scaling function these samples correspond to >> the original samples used in wavelet synthesis. Here sampling means >> >> x_s[n] = <f,phi_n_s>, (2) >> >> where f is the analyzed (sampled) function, phi is the scaling function >> with translation n and scale s. It is obvious that the signal can be >> later perfectly reconstructed from the samples by wavelet synthesis >> (assuming the scaling function matched the scaling function used in the >> original synthesis). >> >> In fact, sinc function is just one possible scaling function (in which >> case one talks about shannon wavelets). This makes traditional sampling >> just a special case of wavelet transform (in single resolution). Note >> that the previous comment about infinite bandwidth does not obviously >> apply to shannon wavelets. >> >> Any comments, or corrections? >> > I'm not a wavelet guru, but if I'm reading your math right you are > constraining yourself to sampling a finite number of wavelets, each of > which may have frequency content going out to infinity, and being able > to perfectly reconstruct the signal. To be exact, I'm constrained to finite resolution and sampling only with _scaling functions_. In single resolution case, there is no need for wavelet functions (see below the correction). They appear when there is need to express the missing information from what can be represented by scaling functions in resolution s when compared to finer resolution s+1. Number of scaling functions are, in fact, countably infinite as every translation is counted as distinct function. > > I'll believe you that this is true*. Actually there is a mistake. First of all eq. (2) is highly redundant. When sampling with scaling functions, the highest resolution sampled at contains all the information of the lower resolutions. Thus equation (1) is bogus. It should have introduced wavelets, but they are irrelevant to this discussion. These are correct versions and restricts the transform to single resolution: f(t) = SUM_n( x[n]*phi(t-n) ) (a) x[n] = <f(t), phi(t-n)> (b) But the basic "claim" holds. > > Where your observation falls down, however, is that there are no > perfect, physically realizable 'wavelet filters' to use -- you can > _synthesize_ a function in some mathematical domain, but you can't go to > and from physical reality with arbitrary wavelets. True, just like there is no perfectly realizable sinc filters. This discussion was purely theoretical and I believe that in theory (given the restrictions posed for scaling function and subsequently, the analyzed function) "wavelet sampling" works as explained. > > I suspect that even if you could make some magic wavelet filter bank > with a finite number of wavelets that you would have to constrain your > signal to be composed only of the wavelets in your set, and any > additional wavelets in the actual signal would 'alias' into your set of > realized wavelets**. Actually, this was my point exactly (or at least one of them). In case of Nyquist-Shannon sampling the set of realized "wavelets" (actually scaling functions) are the translates of the sinc function in single resolution (i.e., in single samplerate). Set of functions that do not alias are those which have correctly restricted bandwidth or, in other words, which are linear combinations of the translated sinc functions. Or mathematically if phi(t) = sinc(t) V0 = span A, where A = { phi(t-n) } then V0 is set of bandlimited functions satisfying Nyquist-Shannon theorem. In general case, V0 is a set called scaling space, where the aliasing condition is defined by the chosen phi(t). f(t) is simply projected to V0 and if after the projection there is left residual, it is called aliasing in case of NS. (In case of "normal" wavelet transform this aliasing is captured by the so called wavelet spaces Wn which are orthogonal to all scaling spaces Vn) As you brought in practical considerations of physical world, then I ask you: Could it be possible than some scaling function could be implemented in hardware more accurately than sinc? I have no idea myself as this really is not my area of expertise. -- Jani Huhtanen Tampere University of Technology, Pori   0 Reply jani.huhtanen (173) 8/25/2006 6:07:01 AM Rick Lyons wrote: > On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com> > wrote: > > >>Kinda off topic -- >> >>A month or two ago there was a spate of postings on these groups >>displaying a profound misunderstanding of how to apply Nyquist's theorem >>to problems of setting sampling or designing anti-alias filters. I >>helped folks out as much as I could, but it really demands an article, >>which I am currently working on. >> > > (snipped) > > Hi, > I just finished posting a long rant > about sampling articles written by Gerard Fonte. > > I just noticed (on the web) that the San > Fernando Valley Engineers' Council Inc. > has awarded Gerard Fonte an "Outstanding > Engineering Achievement Merit Award" for 2006. > > See: > http://engineerscouncil.org/Gallery/EWeekBanquet2006?page=4 > > [-Rick-] > ....and when will their faces and the egg collide?   0 Reply robertbaer (111) 8/25/2006 6:18:47 AM jim wrote: > > Robert Baer wrote: > >>mobi wrote: >> >> >>>Do consider this interesting (atleast for me) example >>> >>>Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately >>>i start sampling from time = 0. What would i get? Aint i statisifying >>>Nyquist here? >>> >> >> Yup! >> Also try sampling at a constant delay from the sine zero crossing. >> That is what happens when people blindly follow a "criteria" without >>knowing the full reason and background. > > > What is what happens? Do you actually know what happens if you actually > try this in a real world context? Set up a speaker generating the Fs/2 > signal. Set up a microphone and and ADC to record the sound at Fs. Are > you claiming that you can adjust the sampling phase to produce a digital > recording of either full scale or zero? That's what in theory should > happen - right? But can you do that in real life? > > -jim > > ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- > http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups > ----= East and West-Coast Server Farms - Total Privacy via Encryption =---- I suggest that you draw the waveforms, selscting some arbitrary but fixed phase relation, then re-draw with a slightly different phase relation.   0 Reply robertbaer (111) 8/25/2006 6:21:43 AM Jani Huhtanen wrote: > Tim Wescott wrote: -- snip -- > > As you brought in practical considerations of physical world, then I ask > you: Could it be possible than some scaling function could be implemented > in hardware more accurately than sinc? I have no idea myself as this really > is not my area of expertise. > > I don't know, because I'm still not clear on the definition of a scaling function. Can you post a URL or two? I think, though, that no matter what you do you'll run into a very basic limitation, which is that you can't take a completely arbitrary signal and throw away an infinite fraction of it without also throwing away an infinite amount of information. The only way that you can take a given signal and throw away an infinite amount of information pertaining to it, and retain all of the information in the original signal, is if the original signal isn't arbitrary, but is guaranteed to have it's information content limited in just the right way to match the manner in which you are throwing away information*. The Nyquist theorem just explains this in the context of the frequency domain, and shows an upper limit on how much information you can expect to retain before you start running into problems. * I contend that this syntax isn't fractured; it's merely complex. None the less, I won't attempt to diagram the sentence unless you pay me. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/25/2006 6:56:58 AM Robert Baer wrote: > Rick Lyons wrote: > >> On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com> >> wrote: >> >> >>> Kinda off topic -- >>> >>> A month or two ago there was a spate of postings on these groups >>> displaying a profound misunderstanding of how to apply Nyquist's >>> theorem to problems of setting sampling or designing anti-alias >>> filters. I helped folks out as much as I could, but it really >>> demands an article, which I am currently working on. >>> >> >> (snipped) >> >> Hi, >> I just finished posting a long rant about sampling articles written >> by Gerard Fonte. >> >> I just noticed (on the web) that the San Fernando Valley Engineers' >> Council Inc. >> has awarded Gerard Fonte an "Outstanding Engineering Achievement Merit >> Award" for 2006. >> >> See: >> http://engineerscouncil.org/Gallery/EWeekBanquet2006?page=4 >> >> [-Rick-] >> > ...and when will their faces and the egg collide? They'll never notice (unless they read this group). Their local boy has been published and has therefore made good, so he gets the award. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/25/2006 6:58:55 AM Jani Huhtanen wrote: .... > As you brought in practical considerations of physical world, then I ask > you: Could it be possible than some scaling function could be implemented > in hardware more accurately than sinc? i dunno, but if it's a general bandlimited function with no other assumption other than being bandlimited to B, i don't think there is a wavelet transform that will encode the same reasonably long finite segment of x(t) that will be as few samples as uniform sampling. now, when you toss in error constraints of some sort, it may very well be that some wavelet decomposition will result in less data for encoding than uniform sampling but there is no issue of quantization error in uniform sampling a la Nyquist/Shannon. this sinc thing can do perfect reconstruction for sampling faster than 2B (no quantization of sample values due to finite word length). no error. S/N = inf. that's hard to exceed. now you might have another basis, not bandlimited to B, that matches the sampling points perfectly and might even not require x(t) being bandlimited, but i can't believe it will match x(t) between samples in general. > I have no idea myself as this really is not my area of expertise. as the wavelet transform is not mine. r b-j   0 Reply rbj (4087) 8/25/2006 7:07:04 AM Tim Wescott wrote: > A month or two ago there was a spate of postings on these groups > displaying a profound misunderstanding of how to apply Nyquist's theorem > to problems of setting sampling or designing anti-alias filters. I > helped folks out as much as I could, but it really demands an article, > which I am currently working on. As I remember it, Nyquist wasn't sampling at all. He was trying to get telegraph pulses through a cable, and wanted to know how close together the pulses could be. Instead of sampling a continuous signal, he wants to send a sampled signal (pulses) though a band limited channel. It happens to be the same math, and so he gets the sampling theorem, also. -- glen   0 Reply gah (12850) 8/25/2006 7:20:59 AM Rick Lyons wrote: .... > > Hi Tim, > > Writing about the effects of "periodic sampling" > is an interesting and educational thing to do. [snipped stories about breaking Nyquist] I don't think you participated, Rick, but I while ago I posted a DSP riddle about regular sampling of periodic and continuous signals with known period (here: http://groups.google.ch/group/comp.dsp/browse_frm/thread/a1ec87ab8645386f/cfc467f0c22e02a1?#cfc467f0c22e02a1). Under those conditions I showed that it is possible to arbitrarily well approximate the periodic signal from the regular samples, given enough time. Further, I showed that this is possible even if the signal is a) not bandlimited, and/or b) the sampling frequency was bounded by some given value (ie. undersampling). The proposed reconstruction process does not involve sinc interpolation, but rather synthesis with truncated Fourier sums. I thought it was rather neat, but reactions here ranged from disbelief to stating that this was trivial. I haven't worked it out yet, but I think the scheme is extendable to the case where the period of the signal is unknown (using two regular samplers with irrational sampling periods). Regards, Andor   0 Reply andor.bariska (1307) 8/25/2006 7:48:07 AM Tim Wescott wrote: > Robert Baer wrote: > >> Rick Lyons wrote: >> >>> On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com> >>> wrote: >>> >>> >>>> Kinda off topic -- >>>> >>>> A month or two ago there was a spate of postings on these groups >>>> displaying a profound misunderstanding of how to apply Nyquist's >>>> theorem to problems of setting sampling or designing anti-alias >>>> filters. I helped folks out as much as I could, but it really >>>> demands an article, which I am currently working on. >>>> >>> >>> (snipped) >>> >>> Hi, >>> I just finished posting a long rant about sampling articles written >>> by Gerard Fonte. >>> >>> I just noticed (on the web) that the San Fernando Valley Engineers' >>> Council Inc. >>> has awarded Gerard Fonte an "Outstanding Engineering Achievement >>> Merit Award" for 2006. >>> >>> See: >>> http://engineerscouncil.org/Gallery/EWeekBanquet2006?page=4 >>> >>> [-Rick-] >>> >> ...and when will their faces and the egg collide? > > They'll never notice (unless they read this group). Their local boy has > been published and has therefore made good, so he gets the award. > Does that also work if he is published in the National Inquirer? :-) Steve   0 Reply steveu (1008) 8/25/2006 8:18:01 AM robert bristow-johnson wrote: > > Jani Huhtanen wrote: > ... >> As you brought in practical considerations of physical world, then I ask >> you: Could it be possible than some scaling function could be implemented >> in hardware more accurately than sinc? > > i dunno, but if it's a general bandlimited function with no other > assumption other than being bandlimited to B, i don't think there is a > wavelet transform that will encode the same reasonably long finite > segment of x(t) that will be as few samples as uniform sampling. Possibly. > > this sinc thing can do perfect reconstruction for sampling faster than > 2B (no quantization of sample values due to finite word length). no > error. S/N = inf. that's hard to exceed. now you might have another > basis, not bandlimited to B, that matches the sampling points perfectly > and might even not require x(t) being bandlimited, but i can't believe > it will match x(t) between samples in general. > I have to think about that some more. It is true that if phi(t) = sinc(t), then x(t-t0) \in V0 for all t0 \in R. I believe also that if phi(t) != sinc(t) then generally it does not work (seems intuitive when thinking about Haar). Perhaps this is where it falls down... > r b-j -- Jani Huhtanen Tampere University of Technology, Pori   0 Reply jani.huhtanen (173) 8/25/2006 8:44:27 AM hi undersample sampling ================= pick two frequencies relatively prime to each other and sample as per useual. then make f amplitude buckets (f = f1*f2) so that all the multiple aliases of frequency are present. f FFT buckets, add f1 frequency spectrum into the first f1 buckets, and then into next f1 buckets, and repeat this f2 times. repeat this with fft of f2 samples, with possible f1 * repeated aliases. using another f1 * f2 buckets. then do convolution, by multiplying both sets of buckets. this will case correlation peak at covergence of alias frequencies. final inverse fft is not an exact sample sequence as you would get if sampling at the one rate of (f1*f2), but for some purposes this does not matter. if you want just a bandpass, then just construct part of the frequency buckets, to convolute, and the adjust the base (frequency shift), and do an inverse fft. this is a downconversion and sampling procedure. cheers   0 Reply jackokring (1001) 8/25/2006 9:11:15 AM CBFalconer wrote: > vasile wrote: > > Tim Wescott wrote: > > > ... snip ... > >> > >> But you can't avoid the issue of providing sufficiently steep > >> skirts on your filters, both in and out. As you get closer and > >> closer to Nyquist in a 'simple' system your filter complexity > >> goes through the roof, as does the difficulty of actually > >> realizing the filters in analog hardware. > > > > I'm not entirely agree with that. There are a lot of analog > > antialising filters, which are quite good near the Nyquist. One > > of them frequently used is the Cebashev filter (eliptical > > filter) which design and implementation is easy up to quite > > high frequencies (say 100-200Mhz, at least tested by myself). > > That's fine if you don't care about phase linearity (time delay). > Chebychev filters are notoriously poor at preserving phase, or > having constant delay characteristics. This results in heavy > distortion of analog waveforms, and will manifest itself as such > effects as overshoot and ringing. A Bessel filter is designed to > minimize this effect, but has much more gentle rejection slopes. Agree. Bessel unfortunately can't be used for high slopes. But with a custom design even the Chebashev can be made to keep the time delay into reasonable limits as long is used far enough from Nyquist limit (in frequency domain). I've seen solutions using FIR filters (24 to 32tap at 16Mhz sampling), but some dirt can't be rejected and still need and auxiliary analogic filter. Not talking about DSP or processor time required by such filter... Vasile   0 Reply piclist9 (17) 8/25/2006 9:27:12 AM Steve Underwood wrote: > CBFalconer wrote: > > vasile wrote: > >> Tim Wescott wrote: > >> > > ... snip ... > >>> But you can't avoid the issue of providing sufficiently steep > >>> skirts on your filters, both in and out. As you get closer and > >>> closer to Nyquist in a 'simple' system your filter complexity > >>> goes through the roof, as does the difficulty of actually > >>> realizing the filters in analog hardware. > >> I'm not entirely agree with that. There are a lot of analog > >> antialising filters, which are quite good near the Nyquist. One > >> of them frequently used is the Cebashev filter (eliptical > >> filter) which design and implementation is easy up to quite > >> high frequencies (say 100-200Mhz, at least tested by myself). > > > > That's fine if you don't care about phase linearity (time delay). > > Chebychev filters are notoriously poor at preserving phase, or > > having constant delay characteristics. This results in heavy > > distortion of analog waveforms, and will manifest itself as such > > effects as overshoot and ringing. A Bessel filter is designed to > > minimize this effect, but has much more gentle rejection slopes. > > > I wonder if he really means Chebyshev or elliptic (Cauer)? They both > ring badly, Of course, I've thinking to Cauer, sorry. Vasile   0 Reply piclist9 (17) 8/25/2006 9:30:30 AM Andor wrote: > Rick Lyons wrote: > > ... >> >> Writing about the effects of "periodic sampling" >> is an interesting and educational thing to do. > > [snipped stories about breaking Nyquist] > > I don't think you participated, Rick, but I while ago I posted a > DSP riddle about regular sampling of periodic and continuous > signals with known period (here: > http://groups.google.ch/group/comp.dsp/browse_frm/thread/a1ec87ab8645386f/cfc467f0c22e02a1?#cfc467f0c22e02a1). > > Under those conditions I showed that it is possible to arbitrarily > well approximate the periodic signal from the regular samples, > given enough time. Further, I showed that this is possible even if > the signal is > a) not bandlimited, and/or > b) the sampling frequency was bounded by some given value (ie. > undersampling). > > The proposed reconstruction process does not involve sinc > interpolation, but rather synthesis with truncated Fourier sums. > I thought it was rather neat, but reactions here ranged from > disbelief to stating that this was trivial. I haven't worked it > out yet, but I think the scheme is extendable to the case where > the period of the signal is unknown (using two regular samplers > with irrational sampling periods). Of course you can reconstruct some signals with slow sampling - it is done all the time in sampling oscilloscopes. This requires a trigger related to the repetitive signal and a moving time delay. But this is not a real-time operation, as is the usual sampled reconstruction of a complete waveform. -- Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net) Available for consulting/temporary embedded and systems. <http://cbfalconer.home.att.net> USE maineline address!   0 Reply cbfalconer (19194) 8/25/2006 12:51:41 PM On 24 Aug 2006 09:52:26 -0700, "robert bristow-johnson" <rbj@audioimagination.com> wrote: > (snipped) > >are any of these online? > Hi R B-J, The Smith article (and all the Letters to the Editor) are probably somewhere on the IEEE website. That's only useful to you if you've won the lottery and can afford to subscribe to the IEEE's XPlore program. The first Fonte article is not online, as far as I can tell. For people who subscribe to the Circuit Cellar magazine, I'll bet that the 2nd Fonte article is available online. The Bonnie baker article is at: http://www.edn.com/article/CA529378.html See Ya', [-Rick-]   0 Reply R 8/25/2006 1:08:33 PM On Fri, 25 Aug 2006 00:20:59 -0700, glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote: >Tim Wescott wrote: > >> A month or two ago there was a spate of postings on these groups >> displaying a profound misunderstanding of how to apply Nyquist's theorem >> to problems of setting sampling or designing anti-alias filters. I >> helped folks out as much as I could, but it really demands an article, >> which I am currently working on. > >As I remember it, Nyquist wasn't sampling at all. He was trying >to get telegraph pulses through a cable, and wanted to know >how close together the pulses could be. > >Instead of sampling a continuous signal, he wants to send >a sampled signal (pulses) though a band limited channel. > >It happens to be the same math, and so he gets the sampling >theorem, also. > >-- glen Hi, you may be right about that. I once read something on the Internet written by a guy who was having lunch (one afternoon at a university cafeteria) with Claude Shannon. The writer said that Shannon stated that it he (Shannon) who named the sampling theorem after Nyquist. See Ya', [-Rick-]   0 Reply R 8/25/2006 1:25:27 PM On 24 Aug 2006 09:52:26 -0700, "robert bristow-johnson" <rbj@audioimagination.com> wrote: > (snipped) > >Rick, i fear that similar stuff is being done in the Wikipedia article. > this guy (whose name is very similar to yours and claims to have Alan >Oppenheim and Ron Schafer as friends) would say to you that "the >converse of the Nyquist-Shannon sampling theorem is not true", meaning >that there are cases where frequency components at or above the Nyquist >frequence can be validly reconstructed under some circumstances. i >think he's talking about bandpass sampling. Hi, How would I go about reading about (1) "this guy", and (2) what he's written about the topic of sampling? Thanks, [-Rick-]   0 Reply R 8/25/2006 1:29:04 PM Tim Wescott wrote: ... > AFAIK Nyquist got his first fame with the analysis of negative feedback > in vacuum tube amplifiers back in the '20s when it was all magic. _Then_ > he got into cahoots with Shannon to make his rate. It's amazing how quickly technology goes from magic to mundane. As you say, negative feedback was magic in the 20s. It wasn't widely used in audio until the late 40s, when new post-war designs began to be produced, and then only in "audiophile" equipment. The console radio-phonographs sold immediately after VJ Day and at least through 1948 were all pre-war designs, late 30s vintage. By the early 50s, with no formal training, I was reworking the guts of Capeharts and Magnavoxes to cut distortion from about 8% at 6 watts to less than 1% at 12 watts. I replaced the original speakers (salvaging their magnets for continues use as power-supply chokes), but otherwise reused the original parts. (Actually, I had some left over when I was done. I saved some of them. Does anyone want a radial-lead body-end-dot carbon resistor?) I lined the cabinets with felt and closed the backs. Usually, I replaced the 78 changer with a Garrard that also played LPs; then I needed to add a phono preamp: a single 12AY7.* Was I in my late teens smarter than the engineers who designed the original circuits when I was not quite ten? No way. I had the benefit of the intensive developments of the war years, encapsulated in the back of the RCA tube manual, in the ARRL handbook, and in books like the MIT Radiation Lab's "Principles of Radar". Jerry ___________________________________________ * The first conversion was for a family friend who generously allowed me to tinker with his Capehart. All the rest were paid projects for people who had heard the original or a later conversion. What began as tinkering led to a profession. "Now I are one." -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/25/2006 1:50:27 PM Tim Wescott wrote: > And where aliasing is a problem, there's more to it than the end-to-end > transfer function -- strictly speaking you can't formulate a > laplace-domain transfer function for a time-varying system, such as a > system that incorporates sampled data. > I would disagree with that; you can formulate it. Using it is difficult except numerically; in my experience. Most any time varying function (including time varying coefficients) has a Laplace and Fourier transform. In the case of finite apature S/H or autozero systems you have to make up fancy equivalent circuits (time domain analogs of thevin equivalent circuits) and then write in transform equivalences. In the case of random noise or signals you have to resort to the power domain S(s)*S*(s) . Althought there is a systematic method for dealing with impulses of any order and position; I have never found a systematic way of creating the above equivalent circuits; for finite apatures and autozero circuit inclusion. Ray   0 Reply rerogers (26) 8/25/2006 2:14:05 PM "Tim Wescott" <tim@seemywebsite.com> wrote in message news:4KSdnezoCuh7FHbZnZ2dnUVZ_r-dnZ2d@web-ster.com... > David Hearn wrote: > >> Tim Wescott wrote: >> >>> Kinda off topic -- >>> >>> A month or two ago there was a spate of postings on these groups >>> displaying a profound misunderstanding of how to apply Nyquist's theorem >>> to problems of setting sampling or designing anti-alias filters. I >>> helped folks out as much as I could, but it really demands an article, >>> which I am currently working on. >>> >>> The misconceptions that I noticed pretty much boiled down to the >>> following two: >>> >>> One, "I need to monitor a signal that happens at X Hz, so I'm going to >>> sample it at 2X Hz". >>> >>> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter >>> with a cutoff of X/2 Hz". >>> >>> I estimate that answering these misconceptions will only take 3-4k >>> words, but I don't want to miss any other big ones. >>> >>> Have you seen any other real howlers that relate to Nyquist, and what >>> you should really be thinking about when you're pondering sampling >>> rates, anti-aliasing filters and/or reconstruction filters? >>> >>> Danke. >> >> >> So, if you need to monitor a signal that occurs at xHz - what frequency >> should you sample it at? >> >> D > > You need to be more than 2X times the highest interesting frequency > component in your periodic wave, which can be quite high in some cases. > You may also have to do some anti-alias filtering. > Tim, I hope you'll be very careful with the "interesting" part. Too often I see it referred to as "frequency of interest" - which is very misleading. I think "interesting" means "has enough energy to have measurable aliases" and "of interest" may mean, to some, "the only part of the signal that I care about" to the exclusion of higher frequency components of significant energy. This thread is so long that I can't really tell if anyone touched on this..... For others: one must sample at a frequency that is greater than 2X the highest frequency *content* - where "content" is a subjective term indicating there is significant enough energy to cause measurable/objectionable aliasing. Fred Fred   0 Reply fmarshallx1 (1639) 8/25/2006 2:35:22 PM glen herrmannsfeldt wrote: > Tim Wescott wrote: > > > A month or two ago there was a spate of postings on these groups > > displaying a profound misunderstanding of how to apply Nyquist's theorem > > to problems of setting sampling or designing anti-alias filters. I > > helped folks out as much as I could, but it really demands an article, > > which I am currently working on. > > As I remember it, Nyquist wasn't sampling at all. He was trying > to get telegraph pulses through a cable, and wanted to know > how close together the pulses could be. > > Instead of sampling a continuous signal, he wants to send > a sampled signal (pulses) though a band limited channel. i think all of this is correct. > It happens to be the same math, and so he gets the sampling > theorem, also. he doesn't get the theorem exclusively (Shannon's name gets attached), but he gets the "Nyquist frequency". wouldn't it be tits to have the "Herrmannsfeldt impedance" ubiquitous in the lit? r b-j   0 Reply rbj (4087) 8/25/2006 2:51:43 PM In article <YKqdnUvHqKY9FHPZnZ2dnUVZ_vidnZ2d@web-ster.com>, Tim Wescott <tim@seemywebsite.com> wrote: [....] >Correct. In fact, any filter that has a frequency response that goes to >zero and stays there must have an impulse response that extends >infinitely into both positive and negative time. That is not true, if you allow a filter to have an infinit delay. It is only if you ever want to see the middle of the output that you have to have a response extending before the input. -- -- kensmith@rahul.net forging knowledge   0 Reply kensmith1 (84) 8/25/2006 3:03:49 PM Fred Marshall wrote: ... > This thread is so long that I can't really tell if anyone touched on > this..... > > For others: one must sample at a frequency that is greater than 2X the > highest frequency *content* - where "content" is a subjective term > indicating there is significant enough energy to cause > measurable/objectionable aliasing. This is an awfully complex subject, with ramifications that are easy to overlook. Even the last statement, "... *content* is a subjective term indicating there is significant enough energy to cause measurable/objectionable aliasing" needs qualifying. To be strict, one needs to add "measurable/objectionable aliasing *into the band of real interest*". Other aliases can be filtered out. Accurate and definitive statements not subject to nit picking are exceedingly hard to make (at least without Wescott's tortured syntax). :-) That's why it's an art. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/25/2006 4:10:49 PM "Jerry Avins" <jya@ieee.org> wrote in message news:iqadnTbd5o2JvHLZnZ2dnUVZ_qCdnZ2d@rcn.net... > Fred Marshall wrote: > > ... > >> This thread is so long that I can't really tell if anyone touched on >> this..... >> >> For others: one must sample at a frequency that is greater than 2X the >> highest frequency *content* - where "content" is a subjective term >> indicating there is significant enough energy to cause >> measurable/objectionable aliasing. > > This is an awfully complex subject, with ramifications that are easy to > overlook. Even the last statement, "... *content* is a subjective term > indicating there is significant enough energy to cause > measurable/objectionable aliasing" needs qualifying. To be strict, one > needs to add "measurable/objectionable aliasing *into the band of real > interest*". Other aliases can be filtered out. Accurate and definitive > statements not subject to nit picking are exceedingly hard to make (at > least without Wescott's tortured syntax). :-) That's why it's an art. > > Jerry Jerry, If it wasn't "into the band of real interest" then it wouldn't be measurable/objectionable. To say more seems like "quantifying" rather than "qualifying" - e.g. "this band vs. that band, etc." I don't know that math and hard work are really artful. One does need to know what one is doing. Knowing what is too big to ignore is calculable most of the time. Fred   0 Reply fmarshallx1 (1639) 8/25/2006 6:30:55 PM Tim Wescott wrote: > Jani Huhtanen wrote: > >> Tim Wescott wrote: > -- snip -- > >> >> As you brought in practical considerations of physical world, then I ask >> you: Could it be possible than some scaling function could be implemented >> in hardware more accurately than sinc? I have no idea myself as this >> really is not my area of expertise. >> >> > I don't know, because I'm still not clear on the definition of a scaling > function. Can you post a URL or two? An Overview of Wavelet Based Multiresolution Analysis Bj�rn Jawerth and Wim Sweldens http://cm.bell-labs.com/who/wim/papers/overview.pdf I was tempted to point you to my thesis, but I refrained from self pimpin' :) > > I think, though, that no matter what you do you'll run into a very basic > limitation, which is that you can't take a completely arbitrary signal > and throw away an infinite fraction of it without also throwing away an > infinite amount of information. The only way that you can take a given > signal and throw away an infinite amount of information pertaining to > it, and retain all of the information in the original signal, is if the > original signal isn't arbitrary, but is guaranteed to have it's > information content limited in just the right way to match the manner in > which you are throwing away information*. > It was not my intention to claim any such thing. Nyquist-Shannon "requires" bandlimitedness, other choice for phi(t) may have different requirements (not necessarily including bandlimitedness). > The Nyquist theorem just explains this in the context of the frequency > domain, and shows an upper limit on how much information you can expect > to retain before you start running into problems. True. -- Jani Huhtanen Tampere University of Technology, Pori   0 Reply jani.huhtanen (173) 8/25/2006 6:34:16 PM On 24 Aug 2006 16:30:24 -0700, "Ron N." <rhnlogic@yahoo.com> wrote: >Jerry Avins wrote: >> jim wrote: >> > >> > Robert Baer wrote: >> >> mobi wrote: >> >> >> >>> Do consider this interesting (atleast for me) example >> >>> >> >>> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately >> >>> i start sampling from time = 0. What would i get? Aint i statisifying >> >>> Nyquist here? >> >>> >> >> Yup! >> >> Also try sampling at a constant delay from the sine zero crossing. >> >> That is what happens when people blindly follow a "criteria" without >> >> knowing the full reason and background. >> > >> > What is what happens? Do you actually know what happens if you actually >> > try this in a real world context? Set up a speaker generating the Fs/2 >> > signal. Set up a microphone and and ADC to record the sound at Fs. Are >> > you claiming that you can adjust the sampling phase to produce a digital >> > recording of either full scale or zero? That's what in theory should >> > happen - right? But can you do that in real life? >> >> Of course you can lock the sampler to the sampled waveform or one of its >> harmonics. Google for "PLL". > >However the phase information fed to the PLL to allow it to lock >would constitute additional samples, thus raising the total sample >rate of all information coming into the system above Fs/2. You >have to count all the samples, not just the ones you label as >"samples". Not really. You can be sampling at exactly Fs/2 but be off phase. If the detector and loop are decent it'll figure out which way to steer the phase without additional samples. It won't always be on the right phase, that's the point of letting it lock, but you don't, theoretically, need more samples to do it. The detector may be hard to sort out depending on the signal, but you don't need more samples. It's common to do this with PSK/QAM signals, where there is only one sample per symbol. You don't ever need to sample higher than that from just a sampling requirement perspective and common detectors will lock the sampling clock quickly to the symbol peaks. Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org   0 Reply eric.jacobsen (2636) 8/25/2006 8:09:08 PM Andor wrote: > > Under those conditions I showed that it is possible to arbitrarily well > approximate the periodic signal from the regular samples, given enough > time. Further, I showed that this is possible even if the signal is > a) not bandlimited, and/or > b) the sampling frequency was bounded by some given value (ie. > undersampling). > > The proposed reconstruction process does not involve sinc > interpolation, but rather synthesis with truncated Fourier sums. I > thought it was rather neat, but reactions here ranged from disbelief to > stating that this was trivial. I haven't worked it out yet, but I think > the scheme is extendable to the case where the period of the signal is > unknown (using two regular samplers with irrational sampling periods). > Andor: If your really interested you might look into the Muntz Polynomial theorems. They provide a way to approximate L2 waveforms. Resolving the equations would allow an almost arbitrary exponential basis, with the coefficients determined by sampled points. I also have some papers on irregular sampling around if your interested. My goal was determining "sampling" points for spectral analysis of IR absorbtions so it doesn't actually match up with this discussion smoothly. Sorry for the side issue, but I really think the Muntz theorems are neat and underutilized. Ray   0 Reply rerogers (26) 8/25/2006 8:24:48 PM Eric Jacobsen wrote: > On 24 Aug 2006 16:30:24 -0700, "Ron N." <rhnlogic@yahoo.com> wrote: > .... snip ... >> >> However the phase information fed to the PLL to allow it to lock >> would constitute additional samples, thus raising the total sample >> rate of all information coming into the system above Fs/2. You >> have to count all the samples, not just the ones you label as >> "samples". > > Not really. You can be sampling at exactly Fs/2 but be off phase. If > the detector and loop are decent it'll figure out which way to steer > the phase without additional samples. It won't always be on the > right phase, that's the point of letting it lock, but you don't, > theoretically, need more samples to do it. The detector may be hard > to sort out depending on the signal, but you don't need more samples. > > It's common to do this with PSK/QAM signals, where there is only one > sample per symbol. You don't ever need to sample higher than that > from just a sampling requirement perspective and common detectors will > lock the sampling clock quickly to the symbol peaks. You are basically describing the action of a sampling oscilloscope. This is not sampling at Fs/2, because the change in phase affects the sampling frequency. -- Some informative links: news:news.announce.newusers http://www.geocities.com/nnqweb/ http://www.catb.org/~esr/faqs/smart-questions.html http://www.caliburn.nl/topposting.html http://www.netmeister.org/news/learn2quote.html   0 Reply cbfalconer (19194) 8/25/2006 10:46:14 PM Fred Marshall wrote: > "Jerry Avins" <jya@ieee.org> wrote in message > news:iqadnTbd5o2JvHLZnZ2dnUVZ_qCdnZ2d@rcn.net... >> Fred Marshall wrote: >> >> ... >> >>> This thread is so long that I can't really tell if anyone touched on >>> this..... >>> >>> For others: one must sample at a frequency that is greater than 2X the >>> highest frequency *content* - where "content" is a subjective term >>> indicating there is significant enough energy to cause >>> measurable/objectionable aliasing. >> This is an awfully complex subject, with ramifications that are easy to >> overlook. Even the last statement, "... *content* is a subjective term >> indicating there is significant enough energy to cause >> measurable/objectionable aliasing" needs qualifying. To be strict, one >> needs to add "measurable/objectionable aliasing *into the band of real >> interest*". Other aliases can be filtered out. Accurate and definitive >> statements not subject to nit picking are exceedingly hard to make (at >> least without Wescott's tortured syntax). :-) That's why it's an art. >> >> Jerry > > Jerry, > > If it wasn't "into the band of real interest" then it wouldn't be > measurable/objectionable. To say more seems like "quantifying" rather than > "qualifying" - e.g. "this band vs. that band, etc." > > I don't know that math and hard work are really artful. One does need to > know what one is doing. Knowing what is too big to ignore is calculable > most of the time. I guess you're right if you read "measurable/objectionable" as "measurable _and_ objectionable". I read it as "measurable _or_ objectionable" without thinking to find a benefit of doubt. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/26/2006 1:02:48 AM RRogers wrote: > Tim Wescott wrote: > > >>And where aliasing is a problem, there's more to it than the end-to-end >>transfer function -- strictly speaking you can't formulate a >>laplace-domain transfer function for a time-varying system, such as a >>system that incorporates sampled data. >> > > I would disagree with that; you can formulate it. Using it is > difficult except numerically; in my experience. Most any time varying > function (including time varying coefficients) has a Laplace and > Fourier transform. In the case of finite apature S/H or autozero > systems you have to make up fancy equivalent circuits (time domain > analogs of thevin equivalent circuits) and then write in transform > equivalences. In the case of random noise or signals you have to > resort to the power domain S(s)*S*(s) . Althought there is a > systematic method for dealing with impulses of any order and position; > I have never found a systematic way of creating the above equivalent > circuits; for finite apatures and autozero circuit inclusion. > Unless you're willing to extend the meaning of 'Transfer Function' to be something like Y = H(s, X) instead of Y(s) = H(s) X(s), then no, strictly speaking, you can't. Are you indeed doing this? You _can_ often make approximations that are more than good enough for many applications, however. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/26/2006 4:37:03 AM Ken Smith wrote: > In article <YKqdnUvHqKY9FHPZnZ2dnUVZ_vidnZ2d@web-ster.com>, > Tim Wescott <tim@seemywebsite.com> wrote: > [....] > >>Correct. In fact, any filter that has a frequency response that goes to >>zero and stays there must have an impulse response that extends >>infinitely into both positive and negative time. > > > That is not true, if you allow a filter to have an infinit delay. It is > only if you ever want to see the middle of the output that you have to > have a response extending before the input. > > I'll agree with you, but only if you'll agree that that's a nit. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/26/2006 4:37:51 AM CBFalconer wrote: > Eric Jacobsen wrote: > > On 24 Aug 2006 16:30:24 -0700, "Ron N." <rhnlogic@yahoo.com> wrote: > > > ... snip ... > >> > >> However the phase information fed to the PLL to allow it to lock > >> would constitute additional samples, thus raising the total sample > >> rate of all information coming into the system above Fs/2. You > >> have to count all the samples, not just the ones you label as > >> "samples". > > > > Not really. You can be sampling at exactly Fs/2 but be off phase. If > > the detector and loop are decent it'll figure out which way to steer > > the phase without additional samples. If you don't hook the detector and loop up to the input signal than it won't lock. If you do hook it up, then that is equivalent to taking at least one more sample (to do a phase comparison or something). So your sample rate is now greater than Fs by whatever measurements the detector made in order to convince you that the PLL is locked. Of if you just looked at the output of the PLL, you would need a lock flag to know whether or not the PLL was locked or not. The lock flag constitutes at least one bit of information which increases the sample rate to Fs + 1 bit > Fs If you don't look at the lock flag, the you won't have any idea what phase the samples were taken at. It could have been a DC level that the PLL couldn't lock to. IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M   0 Reply rhnlogic (1111) 8/26/2006 5:58:45 AM CBFalconer wrote: > Think about it. If you drop 4 out of 5 samples to get tothe 200 > samp/sec, what is the difference (to the receiver) from original > sampling at 200/sec. You have to consider the overall system. Makes sense. The practical consideration is that sometimes the anti-aliasing filter is chosen prior to knowing what might be connected downstream. For example, if some customer comes along wanting to hook up their 10 samples/sec receiver to the output, then they are probably going to be unhappy with the result.   0 Reply mw9936 (11) 8/26/2006 1:34:02 PM > In my opinion that would be a pretty odd system. Sometimes it happens in legacy systems where the ADC stage was built for a certain use, and later on other customers want to hook their receivers up to it. For everything to work best you'd need to modify all fielded units. > > Without opinion, if you interpolate correctly before you decimate then > no, you wouldn't have to take that end-use 50 sample/sec into account at > the initial stage. If you don't, you do. > If I understand you correctly, the downstream system would need to receive ALL samples, then interpolate them for use at the slower 50 sample/sec rate. So in effect they'd still have to act on the data (interpolate) at the faster original rate. This makes sense to me, but the customer may balk at this. There's no ideal solution to this problem. This discussion clarifies some things for me... thanks to all repliers.   0 Reply mw9936 (11) 8/26/2006 1:41:08 PM mw wrote: ... > If I understand you correctly, the downstream system would need to > receive ALL samples, then interpolate them for use at the slower 50 > sample/sec rate. So in effect they'd still have to act on the data > (interpolate) at the faster original rate. This makes sense to me, but > the customer may balk at this. There's no ideal solution to this problem. The high-rate signal must be filtered and decimated before it can become low rate. Those process can be performed by what you call the up-stream system, by the down-stream system, or split between them. Although there may be modules, there is only one signal-flow path. What is non-ideal? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/26/2006 3:26:34 PM RRogers wrote: > Andor wrote: > > > > > Under those conditions I showed that it is possible to arbitrarily well > > approximate the periodic signal from the regular samples, given enough > > time. Further, I showed that this is possible even if the signal is > > a) not bandlimited, and/or > > b) the sampling frequency was bounded by some given value (ie. > > undersampling). > > > > The proposed reconstruction process does not involve sinc > > interpolation, but rather synthesis with truncated Fourier sums. I > > thought it was rather neat, but reactions here ranged from disbelief to > > stating that this was trivial. I haven't worked it out yet, but I think > > the scheme is extendable to the case where the period of the signal is > > unknown (using two regular samplers with irrational sampling periods). > > > Andor: If your really interested you might look into the Muntz > Polynomial theorems. They provide a way to approximate L2 waveforms. > Resolving the equations would allow an almost arbitrary exponential > basis, with the coefficients determined by sampled points. I also have > some papers on irregular sampling around if your interested. My goal > was determining "sampling" points for spectral analysis of IR > absorbtions so it doesn't actually match up with this discussion > smoothly. > Sorry for the side issue, but I really think the Muntz theorems are > neat and underutilized. Thanks for the tip, Ray. Googling quickly revealed a paper titled "The Full M=FCntz Theorem in Lp[0,1] for 0 < p < inf" by Erd=E9lyi and Johnson. This is the first time I've heard about the M=FCntz theorem - very interesting! It might indeed pose the basis for approximating peridodic signals in Lp norm. What else can you say about irregular sampling? Regards, Andor   0 Reply andor.bariska (1307) 8/27/2006 10:10:43 AM robert bristow-johnson wrote: (snip) > he doesn't get the theorem exclusively (Shannon's name gets attached), > but he gets the "Nyquist frequency". wouldn't it be tits to have the > "Herrmannsfeldt impedance" ubiquitous in the lit? There is a story that L'Hopital's rule was formulated by Bernoulli, but L'Hopital bought all Bernoulli's ideas for some period of time, including that one. So there is another way to get your name on a rule or law. Fermi seems to have done pretty well, though. An element Fermium, distance unit (also called the femtometer, conveniently with the same abbreviation), Fermi energy, Fermi momentum, Fermi velocity, and probably more that I can't think of right now. -- glen   0 Reply gah (12850) 8/29/2006 5:08:40 AM In message <h8mdnaihcIJRVm7ZnZ2dnUVZ_tWdnZ2d@comcast.com>, dated Mon, 28 Aug 2006, glen herrmannsfeldt <gah@ugcs.caltech.edu> writes >Fermi seems to have done pretty well, though. An element Fermium, >distance unit (also called the femtometer, conveniently with the same >abbreviation), The metric prefix femto- (10^-15) is named after the Danish word 'femten' - fifteen, not FeRmi -- OOO - Own Opinions Only. Try www.jmwa.demon.co.uk and www.isce.org.uk 2006 is YMMVI- Your mileage may vary immensely. John Woodgate, J M Woodgate and Associates, Rayleigh, Essex UK   0 Reply jmw1 (39) 8/29/2006 6:20:36 AM John Woodgate wrote: > In message <h8mdnaihcIJRVm7ZnZ2dnUVZ_tWdnZ2d@comcast.com>, dated Mon, 28 > Aug 2006, glen herrmannsfeldt <gah@ugcs.caltech.edu> writes >> Fermi seems to have done pretty well, though. An element Fermium, >> distance unit (also called the femtometer, conveniently with the same >> abbreviation), > The metric prefix femto- (10^-15) is named after the Danish word > 'femten' - fifteen, not FeRmi Yes, but the unit of length approximately the diameter of the nucleus was named after Fermi, and is abbreviated to fm. That happens to be 1e-15m. Someone was lucky. -- glen   0 Reply gah (12850) 8/29/2006 10:01:12 AM glen herrmannsfeldt wrote: > robert bristow-johnson wrote: > > (snip) > >> he doesn't get the theorem exclusively (Shannon's name gets attached), >> but he gets the "Nyquist frequency". wouldn't it be tits to have the >> "Herrmannsfeldt impedance" ubiquitous in the lit? > > > There is a story that L'Hopital's rule was formulated by Bernoulli, > but L'Hopital bought all Bernoulli's ideas for some period of time, > including that one. > > So there is another way to get your name on a rule or law. > > Fermi seems to have done pretty well, though. An element Fermium, > distance unit (also called the femtometer, conveniently with the same > abbreviation), Fermi energy, Fermi momentum, Fermi velocity, and > probably more that I can't think of right now. > > -- glen > Fermions, and the Fermi exclusion principal, which you validate every time you fail to sink through the floor. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/29/2006 4:50:22 PM In message <u7OdnTEAMeym7WnZnZ2dnUVZ_omdnZ2d@web-ster.com>, dated Tue, 29 Aug 2006, Tim Wescott <tim@seemywebsite.com> writes >Fermions, and the Fermi exclusion principal, which you validate every >time you fail to sink through the floor. Yes, the FEP makes things firm. (;-) -- OOO - Own Opinions Only. Try www.jmwa.demon.co.uk and www.isce.org.uk 2006 is YMMVI- Your mileage may vary immensely. John Woodgate, J M Woodgate and Associates, Rayleigh, Essex UK   0 Reply jmw1 (39) 8/29/2006 5:06:37 PM Tim Wescott wrote: > ... Fermi exclusion principal, ... Errm, Pauli? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������   0 Reply jya (12872) 8/29/2006 5:13:45 PM Jerry Avins wrote: > Tim Wescott wrote: > > >> ... Fermi exclusion principal, ... > > > Errm, Pauli? > > Jerry Dangit! I'm to young to be senile! Fermi, Pauli, Martini -- what's the difference. Although I don't know if I'd want to be in a bar that had a Martini exclusion principal in effect. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html   0 Reply tim177 (4434) 8/29/2006 5:37:55 PM In message <8Z-dnbRwjrj95mnZnZ2dnUVZ_u2dnZ2d@web-ster.com>, dated Tue, 29 Aug 2006, Tim Wescott <tim@seemywebsite.com> writes >Jerry Avins wrote: > >> Tim Wescott wrote: >> >>> ... Fermi exclusion principal, ... >> Errm, Pauli? >> Jerry > >Dangit! I'm to young to be senile! Three ages of Man; infantile, penile, senile. (;-) > >Fermi, Pauli, Martini -- what's the difference. Have you ever TASTED a dry Fermi? > >Although I don't know if I'd want to be in a bar that had a Martini >exclusion principal in effect. Don't worry; it simply states that only ten Martinis can occupy the same stomach unless it is parallel to the floor. -- OOO - Own Opinions Only. Try www.jmwa.demon.co.uk and www.isce.org.uk 2006 is YMMVI- Your mileage may vary immensely. John Woodgate, J M Woodgate and Associates, Rayleigh, Essex UK   0 Reply jmw1 (39) 8/29/2006 5:52:25 PM In comp.arch.embedded Tim Wescott <tim@seemywebsite.com> wrote: > Fermi, Pauli, Martini -- what's the difference. Easy: two can be counted on to ruin any physical experiment conducted in their presence, whereas the remaining one would be a major asset to have around. -- Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de) Even if all the snow were burnt, ashes would remain.   0 Reply broeker (2903) 8/29/2006 5:57:56 PM Tim Wescott wrote: > Jerry Avins wrote: > > > Tim Wescott wrote: > > > > > >> ... Fermi exclusion principal, ... > > > > > > Errm, Pauli? > > > > Jerry > > Dangit! I'm to young to be senile! > > Fermi, Pauli, Martini -- what's the difference. > > Although I don't know if I'd want to be in a bar that had a Martini > exclusion principal in effect. 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