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I am keen to know that If I have two signals say :

Farend_signal (y[n]) and Nearend_signal (x[n])

and x[n] also contains an echo of y[n] with some delay.

Is there any technique to align these two signals temporally is Spectrogram? For example, any correlation technique to find the temporal displacement between signals after making a spectrogram(STFT) of two signals?

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    $\begingroup$ Techniques you already know in the time domain for template matching, adapted filtering, echo detection, etc. can be transported in a time-scale or time-frequency domain, where the processing is easier due to better signal separation $\endgroup$ – Laurent Duval Nov 28 '20 at 11:07
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    $\begingroup$ In addition to what Laurent said: note that the spectrogram is usually a power thing and thus "erases" phase information; you can't measure fine temporal shifts of signals in a power description of frequency domain. So, I'll go with: using the spectrogram is not a good method. $\endgroup$ – Marcus Müller Nov 28 '20 at 13:06
  • $\begingroup$ @LaurentDuval Thank you so much for the clarification. $\endgroup$ – Khubaib Ahmad Nov 30 '20 at 9:32
  • $\begingroup$ @MarcusMüller Okay I got it. Actually, I was following this question [Eliminate Signal A from Signal B] (dsp.stackexchange.com/questions/7593/…). But I wasn't able to eliminate the signal completely. So, after analysis, I thought that there might be some temporal displacement between the signals so that's why I thought of this technique. $\endgroup$ – Khubaib Ahmad Nov 30 '20 at 9:34
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    $\begingroup$ I agree with @Marcus. I was just supposing you meant a short-time Fourier transform $\endgroup$ – Laurent Duval Nov 30 '20 at 9:37
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You can find a large number of "model-based echo suppression" or "adaptive acoustic echo cancellation" (for the keywords). They often combine a sparsifying transformation (wavelets, time-frequency decompositions) and some form of fitting or adaptation of the model to the time and frequency localization where the echo dwells. Underlying hypotheszs are:

  • the model somehow looks like the echo,
  • the similarity will increase in the transformed domain,
  • this representation will help the morphing, or make is more efficient (faster, etc.)

For voice, you find a look of literature, overviews, etc. You may also look at neighboring domains: vibration-based non-destructive testing or monitoring, ultrasounds. I would mention seimic processing, where echoes are sometimes named multiples (waves bounding several times between layers). Here are two examples I have been involved in. A first one quite fast which uses 1-tap adaptive filters (hint: a complex filter), the second more involved with optimization constraints. They use time-scale wavelets, but could be readily adapted to short-term Fourier transforms or multi-input/multi-output filter banks.

Template-based echo suppression in seismic data

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