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To briefly comment on RBJ's

The Short-Time Fourier Transform (STFT) is an analysis tool that repeatedly applies the Discrete Fourier Transform (DFT or FFT) to short snippets of a longer signal, while sliding the window that selects the snippet of the longer signal that the STFT operates on. The STFT is a function of two independent variables, frequency in the DFT and the time of the center of the sliding window.

I think "repeatedly applies ... operates on" should stand in its own sentence and start like "Its standard implementation", and end with "but it can also be done with strided convolutions". That implementation also lacks a corrective step for some purposes.

"Windowed Fourier transform" is one (and the more common) interpretation, but not the only one - more generally it's a time-frequency decomposition via complex bandpass filters. STFT also isn't exclusively discrete, and even then "frequency in the DFT" is too restrictive, even if not going with DFT freqs is a bad idea.

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  • $\begingroup$ Interesting. Do you have a suggested form of words? Added a community wiki answer. Feel free to edit. $\endgroup$
    – Peter K. Mod
    Aug 4, 2022 at 12:14
  • $\begingroup$ @PeterK. Can we follow dsp.meta or do you just check? $\endgroup$
    – OverLordGoldDragon
    Aug 4, 2022 at 14:33
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    $\begingroup$ I get a notification in a diamond icon in the search bar when meta posts come up. Probably just because I'm a mod. There seems to be a follow button at the bottom of each question on sites I'm not a mod on. $\endgroup$
    – Peter K. Mod
    Aug 4, 2022 at 15:00
  • $\begingroup$ Hay, @OverLordGoldDragon, I hadn't seen this post before when it was fresh. I don't have any problem with mods to any question, answer, or tag that I write as long as the mod is accurate and useful. I completely understand that some things that I write can be improved. $\endgroup$
    – robert bristow-johnson
    May 2 at 16:05
  • $\begingroup$ @robertbristow-johnson I've gone through with an edit, I'm mostly content with it but of course it's open to further discussion. $\endgroup$
    – OverLordGoldDragon
    May 2 at 16:07
  • $\begingroup$ Oh, it's not so bad. the thing about convolving with complex sinusoids or bandpass filtering can just as well be applied to the DFT, or more specifically, Goertzel. $\endgroup$
    – robert bristow-johnson
    May 2 at 16:10

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Here's an attempted update:

The Short-Time Fourier Transform (STFT) is an analysis tool that repeatedly applies the Discrete Fourier Transform (DFT or FFT) to short snippets of a longer signal. Its standard implementation slides the window along the longer signal selecting the snippet that the STFT operates on. The STFT is a function of two independent variables, frequency in the DFT and the time of the center of the sliding window.

Feel free to edit!

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