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My understanding is that a Gabor filter gives us information about when in the input signal does the frequency of interest (equal to the frequency of the sinusoid in the Gabor Filter) occur, thus tackling the inability of the Fourier Transform (FT) to give temporal information.

However, a few videos I saw and articles I read gave me the impression that a short-time Fourier Transform (STFT) does exactly the same thing. So, I'm a bit confused as to when to use what? Do they both serve the same purpose?

N.B. I know that the Gaussian window is smoother and helps deal with edge artifacts, but are there any other differences?

P.S. Assume that the Gabor filter is 1D and time is the independent variable.

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The Gabor transform is just a special case of the STFT, the main difference is, like you said, the Gaussian window.

One characteristics of window functions is that they are $0$ outside a specific range. Gaussian windows aren’t. They tend to $0$ at the edges, which gives the nice property that it is easily invertible, meaning you can fully recover the original signal with the Gabor coefficients (a process called Gabor expansion).

Of course it’s possible to do that with the STFT as well, as long as the COLA constraints are met.

Bottom line, not much difference.

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    $\begingroup$ I don't mean to be pedantic, but since you used Gabor "transform" instead of Gabor "filter" in your answer, are they the same thing and can be used interchangeably? I ask because there have been questions [link] stackoverflow.com/questions/9249694/… in the past asking about the difference between the two, but I still don't understand it enough to distinguish between Gabor filter vs transform. $\endgroup$
    – SNIreaPER
    Commented Sep 15, 2023 at 13:03
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    $\begingroup$ I think this will help. Since you specified 1d signal and asked in a time-frequency transform context, I used the appropriate term Gabor transform. Gabor filters are filters derived from the transform and applied to image processing (for feature exctraction, analysis, etc). $\endgroup$
    – Jdip
    Commented Sep 15, 2023 at 14:39
  • $\begingroup$ @SNIreaPER have I answered your question? $\endgroup$
    – Jdip
    Commented Sep 18, 2023 at 19:15
  • $\begingroup$ Yes, thank you :) $\endgroup$
    – SNIreaPER
    Commented Sep 19, 2023 at 20:17

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