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FFT Analysis for Dummies
C.R.Helmrich
post Apr 4 2010, 18:21
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Back in the days I learned the discrete Fourier transform with this online book. I still recommend it to anyone new to the subject. It uses very simple math and a lot of pictures.

Chris


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Arnold B. Kruege...
post Apr 5 2010, 12:21
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QUOTE (C.R.Helmrich @ Apr 4 2010, 13:21) *
Back in the days I learned the discrete Fourier transform with this online book. I still recommend it to anyone new to the subject. It uses very simple math and a lot of pictures.


Looks like an interesting book.

In it I find the following:

"If the input to a linear system is a sinusoidal wave, the output will also be a sinusoidal wave, and at exactly the same frequency as the input."

This supports a claim I made recently here that a linear system creates no new frequencies from any signal that is fed into it.
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SebastianG
post Apr 5 2010, 16:39
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QUOTE (Arnold B. Krueger @ Apr 5 2010, 12:21) *
This supports a claim I made recently here that a linear system creates no new frequencies from any signal that is fed into it.

Linearity alone isn't sufficient. Your system also needs to be "time invariant" (or "shift invariant", different term, same thing). Unfortunately, people often say just "linear" meaning "linear and time-invariant".

Cheers,
SG
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hypervelocity
post Apr 26 2011, 14:43
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Hello guys,

I'm working on my undergraduate thesis, and our topic revolves around the FFT.

Quick question: How do you pick the appropriate N for the transform? Is there any specific rule in selecting N?
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pdq
post Apr 26 2011, 16:16
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That would depend on the sampling rate of your data and the desired frequency resolution of the transform.
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Arnold B. Kruege...
post May 2 2011, 13:42
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QUOTE (hypervelocity @ Apr 26 2011, 09:43) *
Hello guys,

I'm working on my undergraduate thesis, and our topic revolves around the FFT.

Quick question: How do you pick the appropriate N for the transform? Is there any specific rule in selecting N?



First off, select N large enough to obtain the desired low frequency bandpass. ;-)

The other number to worry about is the number of individual analyses that you nned to average together for your "final answer".

Many of the things that you analyze aren't really all that time-invariant. That is especially true of acoustics, particularly the acoustics of large spaces. One scary thing is the fact that the acoustics of a space can wander around by several dB while you are measuring it. So, you need to average a bunch of measurements to get your results to converge to their mean.
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Natalia
post Jan 12 2012, 08:49
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Hi guys!

I am trying to sort out samples according to their peak frequency, but one sample which I expected to show a certain frequency showed the tallest peak at a frequency twice as high as the one I expected (there is a second but shorter peak at the expected frequency as well). Does it mean something, or it's just a coincidence? Can the fundamental frequency appearing on the spectrogram be doubled due to some logical reasons?

Thank you! smile.gif
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xnor
post Jan 12 2012, 18:10
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QUOTE (Natalia @ Jan 12 2012, 09:49) *
I am trying to sort out samples according to their peak frequency

If I understand you right you're trying to find out which time-domain samples contribute most to certain peaks in the frequency response??
Either that or you're confusing samples with frequency bins.

QUOTE
but one sample which I expected to show a certain frequency showed the tallest peak at a frequency twice as high as the one I expected

One sample doesn't show a certain frequency. An impulse results in a flat line in the frequency domain.

QUOTE
Can the fundamental frequency appearing on the spectrogram be doubled due to some logical reasons?

I'm not sure I understand but it looks like there's a bug in your code that changes the fft size or sampling rate or ...

This post has been edited by xnor: Jan 12 2012, 18:11
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Natalia
post Jan 13 2012, 01:49
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Well, I guess I should've made it clear from the beginning.

It's not audio samples I'm studying; I am doing functional MRI, studying activation of the brain to a certain auditory stimuli (presented every 68 seconds) and I ran independent component analysis on scanned images - it decomposes brain networks into statistically independent spatial maps (components) based upon similarity of their time courses.

So I am running FFT on time courses of each separated component (brain network), and I expect certain components (such as auditory cortex and auditory centers) to have fundamental frequency matching with that of auditory stimulus presentation (i.e., 68 seconds=0.147 Hz), meaning that these networks activate in response to the stimulus.

Almost all of them showed it correctly but one which is very much auditory-looking have only a second tall peak at the desired frequency (0.0147 Hz), and the first tall (the tallest) peak is at 0.296 Hz, which is basically the double of stimulus frequency.

I am sorry if this is not the place I should be asking such questions, but I am very new to FFT and I have now idea if this double frequency peak is just a coincidence or it can happen due to some logical reasons.

I use Matlab to run FFT, and I am sure the script works fine as it showed no problems for the other analyses and components.

Sorry if this explanation took too long smile.gif I will be grateful for any insight on the matter.

Thank you!
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Woodinville
post Jan 13 2012, 02:08
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The irony of this thread being ressurrected is:

http://www.aes.org/sections/pnw/



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Natalia
post Jan 13 2012, 02:55
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Wish I could attend smile.gif
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xnor
post Jan 13 2012, 11:41
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Natalie, do these stimuli cause spikes every 68 seconds or are they really sinusoidal waves with very low frequency such as 0.147 Hz? (btw, 1/68 = 0.0147 Hz)
Anyway, I'm not sure I can be of any help since you said almost all of them looked correctly. I was guessing that your fft size might not be large enough -> too low resolution in the freq. domain, but on the other hand I don't think that your sampling rate (number of measured samples per second) is very high so that seems to be fine too (resolution = Fs/N).
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Ethan Winer
post Jan 13 2012, 17:48
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QUOTE (Woodinville @ Jan 12 2012, 20:08) *


Oh geez, I really wish I could attend.

--Ethan


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Kees de Visser
post Jan 13 2012, 19:03
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QUOTE (Ethan Winer @ Jan 13 2012, 18:48) *
Oh geez, I really wish I could attend.
You're probably not the only one. Will it be recorded ?
BTW, judging by the "Nearby Eateries" it's in Fast Food Town.
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Woodinville
post Jan 14 2012, 23:14
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QUOTE (Kees de Visser @ Jan 13 2012, 10:03) *
QUOTE (Ethan Winer @ Jan 13 2012, 18:48) *
Oh geez, I really wish I could attend.
You're probably not the only one. Will it be recorded ?
BTW, judging by the "Nearby Eateries" it's in Fast Food Town.


It's on Microsoft campus, so kinda ...

We have real restaurants, too.


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C.R.Helmrich
post Jan 14 2012, 23:48
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QUOTE (Natalia @ Jan 13 2012, 02:49) *
I am sorry if this is not the place I should be asking such questions, but I am very new to FFT and I have now idea if this double frequency peak is just a coincidence or it can happen due to some logical reasons.

In audio analysis, it's quite possible to find a frequency which is twice or half as high as the "true" frequency. Since you seem to be new to the subject: have you heard of - or done - windowing and DC removal prior to computing the FFT? And how long (in seconds) is your time course of which you compute the FFT?

Chris

This post has been edited by C.R.Helmrich: Jan 14 2012, 23:50


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Gumboot
post Jan 15 2012, 00:25
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QUOTE (Woodinville @ Mar 28 2010, 00:00) *
Some points, an FFT is not an approximation, nor is it a model. It is a precise transform with a precise inverse, one that obeys power and amplitude conservation both in the time and short-term frequency domain.


I take exception to this. An FFT, like anything else, is a model and/or an approximation if it is used as such. Sometimes 3 is an approximation of pi. There's no fantastic mathematical property that can stop something from being used as a very blunt instrument.
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xnor
post Jan 15 2012, 00:40
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QUOTE (Gumboot @ Jan 15 2012, 01:25) *
I take exception to this. An FFT, like anything else, is a model and/or an approximation if it is used as such. Sometimes 3 is an approximation of pi. There's no fantastic mathematical property that can stop something from being used as a very blunt instrument.

Because 3 is an approximation of pi, pi itself is an approximation? Because 0.3425 + 0.4354 cannot be represented exactly with 32 bit floating numbers, addition is just an approximation? I hope you see where this is heading...

It's an invertible, discrete, linear transformation.

This post has been edited by xnor: Jan 15 2012, 00:44
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Canar
post Jan 15 2012, 01:05
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QUOTE (Ethan Winer @ Jan 13 2012, 08:48) *
Oh geez, I really wish I could attend.
I know exactly how you feel. The sad part is, the way things are going, in a couple months it would be possible for me. Oh well, there will be future PNW meetings. I will come down from Vancouver to attend one sooner or later. wink.gif


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Woodinville
post Jan 15 2012, 01:26
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QUOTE (Gumboot @ Jan 14 2012, 15:25) *
QUOTE (Woodinville @ Mar 28 2010, 00:00) *
Some points, an FFT is not an approximation, nor is it a model. It is a precise transform with a precise inverse, one that obeys power and amplitude conservation both in the time and short-term frequency domain.


I take exception to this. An FFT, like anything else, is a model and/or an approximation if it is used as such. Sometimes 3 is an approximation of pi. There's no fantastic mathematical property that can stop something from being used as a very blunt instrument.



No, an FFT is an orthonormal projection, no matter how it's used. It's not the FFT's fault (it has no violition, so how can it be) if somebody uses it in a particular way.


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Woodinville
post Jan 27 2012, 02:50
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Slide deck and octave scripts are up at www.aes.org/sections/pnw

Will try to get recording somehow.

Still making no sense of the "approximation" thing. An orthonormal transform is what it is.

This post has been edited by Woodinville: Jan 27 2012, 02:51


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neelX
post Jan 27 2012, 11:49
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QUOTE (Woodinville @ Jan 27 2012, 03:50) *
Slide deck and octave scripts are up at www.aes.org/sections/pnw


404 on the two .zip files :/
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Woodinville
post Jan 28 2012, 00:13
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QUOTE (neelX @ Jan 27 2012, 02:49) *
QUOTE (Woodinville @ Jan 27 2012, 03:50) *
Slide deck and octave scripts are up at www.aes.org/sections/pnw


404 on the two .zip files :/


Should be fixed. If you still have trouble let me know and I'll pass it along.


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Woodinville
post Jan 28 2012, 05:19
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.zip files still fubar. Webmaster pinged.


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Woodinville
post Jan 28 2012, 11:56
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.zip fixed.


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