Should I apply some window before FFT if I want to find 5 frequencies in signal? Signal is pure 5 sinusoids + some noise generated during recording on analog cable.

  • 1
    $\begingroup$ If you don't know whether to use window or not, simply use a Hamming window, in 98% of cases its good enough (statistics are made up...) $\endgroup$
    – jojek
    Feb 17 '15 at 17:09
  • $\begingroup$ Are all the sinusoids exactly integer periodic in the FFT window width? $\endgroup$
    – hotpaw2
    Feb 17 '15 at 20:46
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    $\begingroup$ If the measurement is of sufficient length, then you might also want to use Welch's method, which can partially counteract the information loss due to windowing. This will reduce the frequency resolution, but should reduce the contribution of the noise. Just play around with it and see what gives the narrowest peaks. If the resolution is not enough, then you could also try a fit in time domain with the fft results as initial guesses. $\endgroup$
    – fibonatic
    Feb 17 '15 at 21:06

Windowing, in the context of DFT, is used to reduce the side-lobes or spectral leakage which happens because you work with finite length discrete signals.

Now, if is sum of sinusoids that are periodic in the observation time (that means that each sinusoid completes an integer amount of periods), then the DFT will be a series of delta function with no side-lobes.
However, in a more realistic scenario, the DFT of your signal should be effected by the spectral leakage. In that case, it is possible that some of the side-lobes will have greater magnitude than some of the sinusoids and if you try to select the 5 frequencies with the greatest magnitude, you will get the wrong results.
To sum it up simply: Yes, you should use some kind of windowing. It doesn't actually meter which window function you use. As suggested, Hamming window is a good choice.


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