Re: Strange behaviour of FFT

[Quentin Spencer]

I don't have time to write a full explanation right now, but the short 
answer is that this behavior is completely expected, and is due to the 
fundamental assumptions in the mathematical definition of the FFT that 
the signal is infinite and periodic with a period equal to the length of 
the FFT. For this reason the FFT by itself is usually not the best tool 
for spectrum analysis. Most advanced DSP textbooks discuss this issue 
and the various approaches to spectrum estimation that have been 
proposed over the years. These usually involve some form of averaging 
FFTs together. I would suggest looking at the "pwelch" function that is 
included in the octave-forge package as a starting point.

regards,
Quentin


Jörg Kampmann wrote:

> I am using the attached little program in order to test the limits 
> etc. of "fft(a,n)"
>
> I generate a superposition of sinewaves of 0.1 s duration and apply 
> fft on it in order to get the power spectrum of the sinewaves.
>
> Strange things seem to happen, perhaps somebody is able to help me or 
> clarify matters:
>
> when you run the Simulation02 you discover (with 10 Superpositions as 
> indicated in variable "SuperPos") that a 200, 400, 600 etc. Hz you get 
> nice power spectra peaks as expected. However at values in between I 
> get strange effects at the footing area of the power spectra peaks, 
> which you can easily observe.
>
> I assume that stems from the way I construct the variable "ySinewave" 
> and "tone".
>
> I would like to get some practical hints on how to best use fft. The 
> tutorial/documentation does not say much about it ...
>
> Thanks in advance
> Joerg




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