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### newbie: spectral analysis on a single waveform

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```Hi all,   I am playing with amplifier circuits for guitar amps and
evaluating a complex signal as it proceeds through the amplifier.  I am
able to capture the signal at various points with a DSO.  Then with the
DSO software I can do an FFT to see the freq spectrum of the signal.

Here is the problem.  The input signal is complex and decays both in
amplitude and somewhat in frequency.  So I want to do FFT just on a
single waveform.  I have been trying to brush up on FFT (it has been a
long time and many beers since then), and I read that FFT is not
accurate on a single waveform.

Any suggestions?

thanks
Don

```
 0
Reply a8723 (11) 11/5/2006 2:41:33 AM

See related articles to this posting

```d1camero wrote:
> Hi all,   I am playing with amplifier circuits for guitar amps and
> evaluating a complex signal as it proceeds through the amplifier.  I am
> able to capture the signal at various points with a DSO.  Then with the
> DSO software I can do an FFT to see the freq spectrum of the signal.
>
> Here is the problem.  The input signal is complex and decays both in
> amplitude and somewhat in frequency.  So I want to do FFT just on a
> single waveform.  I have been trying to brush up on FFT (it has been a
> long time and many beers since then), and I read that FFT is not
> accurate on a single waveform.

Note that in this line of work, "complex" has a mathematical meaning
that doesn't make sense when applied to a signal on a single wire.
(Complex = real + imaginary.) I presume that you mean "complicated".

It you were faces with a single frequency, you would know what it is. A
Fourier transform picks apart complicated waveforms ans shows its
spectrum. If that's not what you want, what do you want?

Jerry
--
"The rights of the best of men are secured only as the
rights of the vilest and most abhorrent are protected."
- Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������
```
 0
Reply jya (12872) 11/5/2006 4:08:49 AM

```Jerry Avins wrote:

...

> It you were faces with a single frequency, you would know what it is. A
> Fourier transform picks apart complicated waveforms ans shows its
> spectrum. ...

Mt thingers are too fick. That should be:
"It you were faced with a single frequency, you would know what it is. A
Fourier transform picks apart a complicated waveform and shows its
spectrum. ...

Jerry
--
"The rights of the best of men are secured only as the
rights of the vilest and most abhorrent are protected."
- Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������
```
 0
Reply jya (12872) 11/5/2006 4:28:33 AM

```Hmmm...  "complex waveform" is a common term used in physics and
engineering. No imaginary numbers here...

I guess you did not understand my question, let me try again:  I have a
complex waveform I would like to apply FFT to get a spectral analysis.
I have read in a Agilent article that FFT does not work propely against
one cycle of a waveform, that it requires multiple cycles.  Is this
true?  If it is, any suggestions on how I can determine the spectral
analysis of a complex waveform that only has a single cycle?

```
 0
Reply a8723 (11) 11/5/2006 6:43:58 AM

```"d1camero" <a8723@cameronsoftware.com> wrote in message
> Hmmm...  "complex waveform" is a common term used in physics and
> engineering. No imaginary numbers here...
>
> I guess you did not understand my question, let me try again:  I have a
> complex waveform I would like to apply FFT to get a spectral analysis.
> I have read in a Agilent article that FFT does not work propely against
> one cycle of a waveform, that it requires multiple cycles.  Is this
> true?  If it is, any suggestions on how I can determine the spectral
> analysis of a complex waveform that only has a single cycle?
>

You can average the FFT and overlap it. Something like

S(i) = beta*S(i-1)+X(i)X*(i)*(1-beta)

where beta is a forgetting factor and S is the Spectrum,X is the freq vector
at index i. Let beta =0.98 or experiment with it. make it smaller for
tracking purposes. Here X* mean complex conjugate.

M.

--
Posted via a free Usenet account from http://www.teranews.com

```
 0

```d1camero wrote:
> Hi all,   I am playing with amplifier circuits for guitar amps and
> evaluating a complex signal as it proceeds through the amplifier.  I am
> able to capture the signal at various points with a DSO.  Then with the
> DSO software I can do an FFT to see the freq spectrum of the signal.
>
> Here is the problem.  The input signal is complex and decays both in
> amplitude and somewhat in frequency.  So I want to do FFT just on a
> single waveform.  I have been trying to brush up on FFT (it has been a
> long time and many beers since then), and I read that FFT is not
> accurate on a single waveform.

What do you mean by a single waveform? Do you mean that you want to
capture the same time sequence at successive points in your amplifier,
and then do an FFT on each capture? You could do that if you could
store it in an arbitrary waveform generator and make it repeat, or just
record it on a PC and use wave edit software to make it loop.
If you're just looking for frequency response information, you could
get it by putting white noise into the input and then doing an FFT on
the noise at various points in the amplifier. If you're looking for
spectrum evidence of distortion, you could get that by a repeating loop
of signals strong enough to cause the distortion.
What information do you expect to get from the FFTs?
--
John

```
 0
Reply quiasmox (41) 11/5/2006 8:45:36 PM

```d1camero wrote:
> Hi all,   I am playing with amplifier circuits for guitar amps and
> evaluating a complex signal as it proceeds through the amplifier.  I am
> able to capture the signal at various points with a DSO.  Then with the
> DSO software I can do an FFT to see the freq spectrum of the signal.
>
> Here is the problem.  The input signal is complex and decays both in
> amplitude and somewhat in frequency.  So I want to do FFT just on a
> single waveform.  I have been trying to brush up on FFT (it has been a
> long time and many beers since then), and I read that FFT is not
> accurate on a single waveform.
>
> Any suggestions?
>
> thanks
> Don
>

Suggestions? Yes :)
You may be asking "wrong" question ;)
[I've cheated by waiting for Jerry & "Major Misunderstanding" to reply]

I suspect you want to look at *HOW* signal decays in time *&* frequency

Try a SEQUENCE of FFT's
If decay time constant is 1 second, look at 200 msec of data at 100 msec
intervals
Plot in pseudo 3-D (waterfall)

Not sure how useful result will be. Should give hints about further

Just remember -- advice may be worth what you paid

```
 0
Reply rowlett10 (1881) 11/5/2006 8:55:50 PM

```d1camero wrote:
> Hmmm...  "complex waveform" is a common term used in physics and
> engineering. No imaginary numbers here...
>
> I guess you did not understand my question, let me try again:  I have a
> complex waveform I would like to apply FFT to get a spectral analysis.
> I have read in a Agilent article that FFT does not work propely against
> one cycle of a waveform, that it requires multiple cycles.  Is this
> true?  If it is, any suggestions on how I can determine the spectral
> analysis of a complex waveform that only has a single cycle?

The problem with the FFT is that the first bin will be the fundamental
(single cycle) and the next bin will be 2x that (2 cycles). If you only
have one cycle your resolution is terrible. Try using the Chirp-Z
transform, which will allow you to examine a narrow freq band.

Tom

```
 0
Reply soar2morrow (22) 11/6/2006 1:03:35 AM

```d1camero wrote:
> Hmmm...  "complex waveform" is a common term used in physics and
> engineering. No imaginary numbers here...
>
> I guess you did not understand my question, let me try again:  I have a
> complex waveform I would like to apply FFT to get a spectral analysis.
> I have read in a Agilent article that FFT does not work propely against
> one cycle of a waveform, that it requires multiple cycles.  Is this
> true?  If it is, any suggestions on how I can determine the spectral
> analysis of a complex waveform that only has a single cycle?

I'm not sure what you mean by a single cycle. The fundamental frequency
of a repeating waveform is the reciprocal of the repetition rate; all
other frequencies are multiples (harmonics) of that. The Fourier
transform of one cycle of that needs no window and gives the same result
as 2, 3, ..., n cycles of the same waveform. Signals that decay are not
in general repetitive.

Jerry
--
"The rights of the best of men are secured only as the
rights of the vilest and most abhorrent are protected."
- Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������
```
 0
Reply jya (12872) 11/6/2006 3:55:03 AM

```Thanks all for the feedback.  Some of this will help.

Jerry,  I am not sure why you are confused, but no matter, as others
have helped out.

Don

```
 0
Reply a8723 (11) 11/8/2006 12:21:04 AM

```d1camero wrote:
> Hmmm...  "complex waveform" is a common term used in physics and
> engineering. No imaginary numbers here...
>
> I guess you did not understand my question, let me try again:  I have a
> complex waveform I would like to apply FFT to get a spectral analysis.
> I have read in a Agilent article that FFT does not work propely against
> one cycle of a waveform, that it requires multiple cycles.  Is this
> true?  If it is, any suggestions on how I can determine the spectral
> analysis of a complex waveform that only has a single cycle?

An FFT of a single cycle should work just fine as long as there
is no content that is not perfectly harmonically related to
the fundamental, and the FFT aperature is exactly one period
in length.  (Some music/sound synthesis tools work this way).
However, if your signal is decaying in amplitude and frequency,
this implies some frequency content inharmonic (or subharmonic)
to your fundamental, and that the fundamental period itself may
not be precisely determinate or defined.

If a window is used (other than the rectangular one inherent
to an FFT implementation) then you also need more repeated
cycles to make up for the information which a non-rectangular
window removes.

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

```
 0
Reply rhnlogic (1111) 11/8/2006 1:28:36 AM

```Ron N. wrote:
> d1camero wrote:
>> Hmmm...  "complex waveform" is a common term used in physics and
>> engineering. No imaginary numbers here...
>>
>> I guess you did not understand my question, let me try again:  I have a
>> complex waveform I would like to apply FFT to get a spectral analysis.
>> I have read in a Agilent article that FFT does not work propely against
>> one cycle of a waveform, that it requires multiple cycles.  Is this
>> true?  If it is, any suggestions on how I can determine the spectral
>> analysis of a complex waveform that only has a single cycle?
>
> An FFT of a single cycle should work just fine as long as there
> is no content that is not perfectly harmonically related to
> the fundamental, and the FFT aperature is exactly one period
> in length.

If those conditions aren't met, it's not a single cycle. What am I
missing here?

>             (Some music/sound synthesis tools work this way).
> However, if your signal is decaying in amplitude and frequency,
> this implies some frequency content inharmonic (or subharmonic)
> to your fundamental, and that the fundamental period itself may
> not be precisely determinate or defined.
>
> If a window is used (other than the rectangular one inherent
> to an FFT implementation) then you also need more repeated
> cycles to make up for the information which a non-rectangular
> window removes.

Jerry
--
"The rights of the best of men are secured only as the
rights of the vilest and most abhorrent are protected."
- Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������
```
 0
Reply jya (12872) 11/8/2006 10:09:54 PM

11 Replies
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