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I have a couple of questions regarding windowed FFTs:

  1. Why is the noise floor higher with windowed FFTs (according to Wikipedia's spectral leakage page, anyway), when the whole point of windowing is to reduce side lobes?

  2. I realize that different windows are better for different things, but is there a window that is considered to be the best all-around window for spectrum analysis? Alternatively, is there a better way to do spectrum analysis than windowed FFTs? It would have to be a DSP approach (i.e. I can't do an array of analog filters), but within that constraint I am game for different solutions.

Thanks for your time in reading this.

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  • $\begingroup$ For future reference, a windowed Fourier transform is called a short-time Fourier transform, or STFT for short. $\endgroup$
    – Emre
    Commented Mar 25, 2012 at 0:57

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A non-rectangular window will remove "noise" from distant bins at the cost of adding more "noise" to the immediately adjacent bins to a narrow-band spectrum peak. The sum of both these spectral leakage effects is greater than zero for a non-rectangular window. So if you count the raising of the level total of all adjacent bins as noise, then the S/N ratio is lowered.

Some people don't care about the bins immediately adjacent to a spectrum peak (their spectral peaks are a priori assumed to be widely spaced; and/or they interpret, interpolate, or phase-vocoder adjust the energy out of those adjacent bins back into the central peak bin), so for those purposes, the reduced far-side-lobe energy means less noise.

Another reason for a lower S/N ratio is that windowing of quantized data is an informationally lossy process, and these (re)quantization losses can also be considered a form of noise.

"Best" is relative to some weighting of quality metrics, and different users may have very different weightings. If you don't have a set of prioritized design goals for which to optimize a window, then you may not have a strong reason to not just use a Von Hann window.

Depending on your data source and your needs, using just some windowed FFTs may not even be a good form of spectrum analysis, much less the best possible. Or the opposite.

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  • $\begingroup$ Thanks. The SNR comments make a lot of sense. How could I find out more about the "interpret, interpolate, or phase-vocoder adjust the energy..." algorithms? Also, you seem to allude to better spectrum analysis methods at the end. Is there anything in particular you had in mind? $\endgroup$
    – Jim Clay
    Commented Feb 7, 2012 at 13:46
  • $\begingroup$ Those might make good questions. Or, depending on the details, they might be dups here. $\endgroup$
    – hotpaw2
    Commented Feb 7, 2012 at 16:37

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