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Why do we want to minimize the difference between the two signals the original one and the modified one when all we want is the modified constructed signal? What is the purpose of making it the minimization problem? Are we trying to save the phase information as the amplitude is anyway going to be updated if we are doing for example decibel conversion for some normalization method as follows?

Decibel Converted signal = $10*log_{10}\frac{signal}{baseline}$ in time-frequency domain.

What constraints should be applied while reconstructing a signal from the above-modified signal and why?

Thanks for answering in advance.

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  • $\begingroup$ what modification are you trying to do with the STFT? STFT is not, in and of itself, an algorithm. by itself, all it accomplishes is "perfect reconstruction" if you apply it correctly. $\endgroup$
    – robert bristow-johnson
    Apr 8, 2020 at 5:39
  • $\begingroup$ @sudhakar Mishra, The reconstruction should be done on raw fft data, not on the decibel converted representation of the data. Once you modifiy fft data, you're changing not only the amplitude but also the phase of the original signal and it's possible that such a signal doesn't even exist (at least not within the constraints of the bandwidth of the original signal). For this reason, you want to minimize the difference (i.e. the error) between the modified and original signal. $\endgroup$
    – dsp_user
    Apr 8, 2020 at 5:43
  • $\begingroup$ Anyway, the standard approach to this problem is implementing the Griffin - Lim algorithm pdfs.semanticscholar.org/14bc/…. $\endgroup$
    – dsp_user
    Apr 8, 2020 at 5:52
  • $\begingroup$ Thanks very much for the response. I got the idea. I will study about phase reconstruction algorithm such as Griffin-Lim. $\endgroup$
    – sudhakar Mishra
    Apr 9, 2020 at 6:08
  • $\begingroup$ However, I am looking for your comment on the size of overlap to reconstruct phase information given only the magnitude information of the modified signal. If there is any good reference to guide the decision on the overlap, sharing it will be a lot helpful. $\endgroup$
    – sudhakar Mishra
    Apr 9, 2020 at 6:11

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