f

#### Group delay in Matlab

```Dear all

I not very familiar with filter design in Matlab and I am probably missin
something when it comes to "group delay". My problem comes as follows.

From what I have understood, if I have a filter such that its group dela
response (plotted with grpdelay[b,a] in matlab with a,b the filte
coefficients) provides 17 as the group delay (in samples) at f=0.1
(normalized frequency so f=0.14*fs/2=0.14*500=70Hz, sampling frequenc
being 1000 Hz) then passing a sinusoid whose frequency is 70Hz through th
filter I should get at the output the same sinusoid (assuming gain is one
delayed by 17 samples.

But it not what I obtain! I have made a lot of tests with different inpu
frequency in the range [0...fs/2] and I always get a smaller delay tha
what I should expect from the group delay response of the filter.

Does anyone have an explaination to provide me?
It sounds to me really basic and I am really wasting my time with it!!!

Gabriel

```
 0
9/18/2006 4:27:52 PM
comp.dsp 20333 articles. 1 followers. allnor (8510) is leader.

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```gab said the following on 18/09/2006 17:27:
> Dear all
>
> I not very familiar with filter design in Matlab and I am probably missing
> something when it comes to "group delay". My problem comes as follows.
>
> From what I have understood, if I have a filter such that its group delay
> response (plotted with grpdelay[b,a] in matlab with a,b the filter
> coefficients) provides 17 as the group delay (in samples) at f=0.14
> (normalized frequency so f=0.14*fs/2=0.14*500=70Hz, sampling frequency
> being 1000 Hz) then passing a sinusoid whose frequency is 70Hz through the
> filter I should get at the output the same sinusoid (assuming gain is one)
> delayed by 17 samples.
>
> But it not what I obtain! I have made a lot of tests with different input
> frequency in the range [0...fs/2] and I always get a smaller delay than
> what I should expect from the group delay response of the filter.
>
> Does anyone have an explaination to provide me?
> It sounds to me really basic and I am really wasting my time with it!!!

I think you are confusing group delay and phase delay.  Phase delay is
defined as:

t = phi/omega

whereas group delay is:

t = d phi / d omega

[i.e. the derivative].

Phase delay is the absolute delay at a given frequency, and I think this
is what you were expecting from your simulation.

--
Oli
```
 0
catch (918)
9/18/2006 4:57:28 PM
```gab wrote:

> Dear all
>
> I not very familiar with filter design in Matlab and I am probably missing
> something when it comes to "group delay". My problem comes as follows.
>
> From what I have understood, if I have a filter such that its group delay
> response (plotted with grpdelay[b,a] in matlab with a,b the filter
> coefficients) provides 17 as the group delay (in samples) at f=0.14
> (normalized frequency so f=0.14*fs/2=0.14*500=70Hz, sampling frequency
> being 1000 Hz) then passing a sinusoid whose frequency is 70Hz through the
> filter I should get at the output the same sinusoid (assuming gain is one)
> delayed by 17 samples.
>
> But it not what I obtain! I have made a lot of tests with different input
> frequency in the range [0...fs/2] and I always get a smaller delay than
> what I should expect from the group delay response of the filter.
>

Of course you have taken into account that 17 samples is ~2.7 samples over
the wavelength? Thus, it might seem that the delay is smaller (i.e., 2.7).

> Does anyone have an explaination to provide me?
> It sounds to me really basic and I am really wasting my time with it!!!

If you truly are interested in how much a sine wave is delayed then you
should use the phase delay as Oli has advised you. However, if you're
interested in the delay of bandlimited signal around f=0.14, then group
delay is the weapon of choice (assuming that the phase is sufficiently
linear around f=0.14)

Check this link for an introduction to subject:
http://ccrma.stanford.edu/~jos/filters/Phase_Response_Applications.html

>
> Gabriel

--
Jani Huhtanen
```
 0
9/18/2006 6:00:35 PM
```What's your application here?  What type of filter is this?

* Group name: RealTime_Signal_and_Control

Jani Huhtanen wrote:
> gab wrote:
>
> > Dear all
> >
> > I not very familiar with filter design in Matlab and I am probably missing
> > something when it comes to "group delay". My problem comes as follows.
> >
> > From what I have understood, if I have a filter such that its group delay
> > response (plotted with grpdelay[b,a] in matlab with a,b the filter
> > coefficients) provides 17 as the group delay (in samples) at f=0.14
> > (normalized frequency so f=0.14*fs/2=0.14*500=70Hz, sampling frequency
> > being 1000 Hz) then passing a sinusoid whose frequency is 70Hz through the
> > filter I should get at the output the same sinusoid (assuming gain is one)
> > delayed by 17 samples.
> >
> > But it not what I obtain! I have made a lot of tests with different input
> > frequency in the range [0...fs/2] and I always get a smaller delay than
> > what I should expect from the group delay response of the filter.
> >
>
> Of course you have taken into account that 17 samples is ~2.7 samples over
> the wavelength? Thus, it might seem that the delay is smaller (i.e., 2.7).
>
> > Does anyone have an explaination to provide me?
> > It sounds to me really basic and I am really wasting my time with it!!!
>
> If you truly are interested in how much a sine wave is delayed then you
> should use the phase delay as Oli has advised you. However, if you're
> interested in the delay of bandlimited signal around f=0.14, then group
> delay is the weapon of choice (assuming that the phase is sufficiently
> linear around f=0.14)
>
> Check this link for an introduction to subject:
> http://ccrma.stanford.edu/~jos/filters/Phase_Response_Applications.html
>
> >
> > Thanks for your help
> > Gabriel
>
> --
> Jani Huhtanen

```
 0
frank.agee (26)
9/19/2006 8:30:45 AM
```What's your application here?  What type of filter is this?

* Group name: RealTime_Signal_and_Control

Jani Huhtanen wrote:
> gab wrote:
>
> > Dear all
> >
> > I not very familiar with filter design in Matlab and I am probably missing
> > something when it comes to "group delay". My problem comes as follows.
> >
> > From what I have understood, if I have a filter such that its group delay
> > response (plotted with grpdelay[b,a] in matlab with a,b the filter
> > coefficients) provides 17 as the group delay (in samples) at f=0.14
> > (normalized frequency so f=0.14*fs/2=0.14*500=70Hz, sampling frequency
> > being 1000 Hz) then passing a sinusoid whose frequency is 70Hz through the
> > filter I should get at the output the same sinusoid (assuming gain is one)
> > delayed by 17 samples.
> >
> > But it not what I obtain! I have made a lot of tests with different input
> > frequency in the range [0...fs/2] and I always get a smaller delay than
> > what I should expect from the group delay response of the filter.
> >
>
> Of course you have taken into account that 17 samples is ~2.7 samples over
> the wavelength? Thus, it might seem that the delay is smaller (i.e., 2.7).
>
> > Does anyone have an explaination to provide me?
> > It sounds to me really basic and I am really wasting my time with it!!!
>
> If you truly are interested in how much a sine wave is delayed then you
> should use the phase delay as Oli has advised you. However, if you're
> interested in the delay of bandlimited signal around f=0.14, then group
> delay is the weapon of choice (assuming that the phase is sufficiently
> linear around f=0.14)
>
> Check this link for an introduction to subject:
> http://ccrma.stanford.edu/~jos/filters/Phase_Response_Applications.html
>
> >
> > Thanks for your help
> > Gabriel
>
> --
> Jani Huhtanen

```
 0
frank.agee (26)
9/19/2006 8:30:52 AM
```gab wrote:
> Dear all
>
> I not very familiar with filter design in Matlab and I am probably missing
> something when it comes to "group delay". My problem comes as follows.
>
> From what I have understood, if I have a filter such that its group delay
> response (plotted with grpdelay[b,a] in matlab with a,b the filter
> coefficients) provides 17 as the group delay (in samples) at f=0.14
> (normalized frequency so f=0.14*fs/2=0.14*500=70Hz, sampling frequency
> being 1000 Hz) then passing a sinusoid whose frequency is 70Hz through the
> filter I should get at the output the same sinusoid (assuming gain is one)
> delayed by 17 samples.
>
> But it not what I obtain! I have made a lot of tests with different input
> frequency in the range [0...fs/2] and I always get a smaller delay than
> what I should expect from the group delay response of the filter.
>
> Does anyone have an explaination to provide me?
> It sounds to me really basic and I am really wasting my time with it!!!

As others have already stated, there may be issues with the sinusoidal
period vs the delay, or confusion with phase velocity.

Yet another potential issue is whether the group velocity makes sense
for monochromatic signals. Group velocity is defined as

vg = dw/dk

where k is wavenumber and w is the angular frequency.

Since there are differentials involved, the signal necessarily
needs to be broad-band, which a single sinusoidal is not.

Maybe the group velocity is easier to come to terms with if
you apply a broad-band pulse to the system.

As for wasting your time: These issues are deceptively
simple. I spent 3 years pondering such questions before
finding some explanations I could accept. Look for a paper
by Johan Leander in the Journal of the Acoustical Society
of America, late -95 or -96, to become even more confused...

Rune

```
 0
allnor (8510)
9/19/2006 9:33:55 AM
```Thank you for your guidance,

Of course it is the concept of "phase delay" which applies to a singl
sinusoide.

That solves one problem.

But if now we consider a baseband signal (I am actually working with a
OFDM signal DVB-T standard 2k mode, at the baseband stage after makin
IFFT of the symbols, and convolution with the pulse shape function).
want to filter out all the frequencies which come from sampling at highe
speed (pulse shape sampled at fs=365 MHz) in the frequency domain and kee
only the signal of interest at baseband (0 to fmax=3.8 MHz).

I use a butterworth filter with cutoff frequency 18MHz and order 13.

From what I have read (c
http://ccrma.stanford.edu/~jos/filters/Derivation_Group_Delay_Modulation.html
I should check first that the phase response is linear between 0 and 3.
MHz and if yes the delay of the signal after the filter should be equal t
the group delay taken at 0 frequency that is to say in the case o
butter[13,1/20] 57 samples!

Am I correct or am I missing again something?

If this is true I am still misunderstanding something since by refering t
the pape
http://www.ece.gatech.edu/research/labs/sarl/tutorials/OFDM/Tutorial_web.pdf#search=%22ofdm%20simulation%20using%20matlab%2
it is said (page 9) that the delay produced by filtering is 64!!! I canno
get this!

Thanks to let me know if you have further clear view on that point.

Gab

```
 0
9/19/2006 11:45:15 AM

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When configuring a T1 and setting up the timeslots you have an option to set the channel group group number. What exactly does the "channel-group" group number do? Normally, I plug in 1, but you can set it from 0-23. channel-group ?? timeslots 1-24 speed 64 (?? is where the group number would go.) Thanks Amy. On 16 Dec 2004 10:53:42 -0800, amyl@paxemail.com wrote: ~ When configuring a T1 and setting up the timeslots you have an option ~ to set the channel group group number. What exactly does the ~ "channel-group" group number do? Normally, I plug in 1, but you can ~ set it from 0-23. ~ ~ channel-group ?? timeslots 1-24 speed 64 ~ (?? is where the group number would go.) ~ ~ Thanks ~ Amy. The channel-group number becomes part of the name of the serial interface you create. For example, if you do this: controller T1 2 channel-group 3 timeslots 1-24 speed 64 then this creates an interface called "Serial 2:3" You can configure multiple channel-groups (and/or ds0-groups if your platform supports it), so pick a unique channel-group/ ds0-group ID for each such group ... e.g. controller t1 2 channel-group 0 timeslots 1-4 speed 64 channel-group 1 timestots 5-12 speed 64 ds0-group 2 timeslots 13-24 type e&m-fgb Aaron ...

Is this group only a Google group?
Hello, I'm discovering APL and I posted a question yesterday on the comp.lang.apl = nntp group. While searching for more information about APL, I stumbled upon= this Google group. I see that it has the same posts than the nntp group, b= ut the last nntp post is from October 1st, 2014. I'm thus wondering if there is are synchronization issues between nntp and = the Google group, or if the problem is with my nntp provider. Thanks, Alan Hi, comp.lang.apl is definitely a usenet group. Many providers aren't retaining many newsgroups long enough and also seem to ...

[News] Windows Vista: Delays, Delays, More Delays and Doubt
Microsoft's Vista faces delays as public tests continue ,----[ Quote ] | David Bradshaw, principal analyst for Ovum, the technology research | group, said that delays to the full release of Vista remained a danger, | noting that such testing programmes are becoming increasingly normal. He | said that public testing programmes were useful in highlighting problems | of compatibility, where the software fails to work properly with certain | printers, software programs or hardware. | | Although the discovery of a problem could force a rewrite, Mr Bradshaw | said, "it would have to be a...

Question about DSP in Matlab (beginner)
Hi, I'm starting to learn DSP (Matlab )and I have two questions about it, maybe someone can help me out? I'm trying to measure a frequency from an Audio Device and I'm using FFT to transform it from the time domain to the frequency domain. But I am doing a downsample before the FFT. But you can also do it after the FFT. Do you know what would be the most efficient (before or after)? And why? Another question, I am using zero padding to increase my system resolution (up to 50Hz). My frame length is N=256 and sample frequency fs= 44100 Hz. So 44100/50 = 882, so I need to add 626 zeroes (to 256 frame length) to get 50 Hz resolution, I hope this is correct? I believe this is done for FFT. But is this the same for the DFT? Thank you and regards, --------------------------------------- Posted through http://www.DSPRelated.com >Hi, > >I'm starting to learn DSP (Matlab )and I have two questions about it, >maybe someone can help me out? > >I'm trying to measure a frequency from an Audio Device and I'm using FFT >to transform it from the time domain to the frequency domain. But I am >doing a downsample before the FFT. But you can also do it after the FFT. >Do you know what would be the most efficient (before or after)? And >why? > >Another question, I am using zero padding to increase my system >resolution >(up to 50Hz). My frame length is N%6 and sample frequency fs= 44100 >...

Filter Design, group delay
Hello, I am looking for a way to obtain the lowest group delay. The specifications are; Lowpass filter fpass=1kHz with 3dB Ripple fstop=4kHz Attenuation 60dB (between 4kHz and 20kHz or between 4kHz and 97.5kHz) with sampling frequency: 195kHz up to 1kHz linear phase and constant group delay (needed) If I use Generalized Equiripple FIR filter of Matlab fda toolbox, th minimum order is 115 (so 57.5 Tabs delay) Is it possible to obtain a new filter which has a delay less than 57. Tabs for the given specifications? Best Regards Gokhan On 12 Okt, 04:58, "gapaydin" <apadi...@yahoo.com> wrote: > Hello, > > I am looking for a way to obtain the lowest group delay. > The specifications are; > > Lowpass filter > fpass=1kHz with 3dB Ripple > fstop=4kHz > Attenuation 60dB (between 4kHz and 20kHz or between 4kHz and 97.5kHz) > with sampling frequency: 195kHz > up to 1kHz linear phase and constant group delay (needed) > > If I use Generalized Equiripple FIR filter of Matlab fda toolbox, the > minimum order is 115 (so 57.5 Tabs delay) > > Is it possible to obtain a new filter which has a delay less than 57.5 > Tabs for the given specifications? I would be very surprised if you can reduce the group delay significantly. Since you require constant group delay you are commited to symmetric FIR filters. Which means that the task is to design the shortest symmetric FIR filter which attains the spec. You may be able to s...

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