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.

link|improve this question
For future reference, a windowed Fourier transform is called a short-time Fourier transform, or STFT for short. – Emre Mar 25 at 0:57
feedback

1 Answer

up vote 4 down vote accepted

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.

link|improve this answer
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? – Jim Clay Feb 7 at 13:46
Those might make good questions. Or, depending on the details, they might be dups here. – hotpaw2 Feb 7 at 16:37
feedback

Your Answer

 
or
required, but never shown

Not the answer you're looking for? Browse other questions tagged or ask your own question.