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There are many explanations of the phase vocoder online, but they are either a bit light on the details "just unwrap the phase!" or using signal processing terminology and electrical diagrams (this tutorial being the most popular link apparently).

I am pretty comfortable with analysis and have a decent understanding of Fourier analysis. For instance I understand what the STFT is, and how to reconstruct a signal from it. I know the proof of the Nyquist-Shannon theorem, etc.

Could someone explain to me (or point me towards an explanation of) the phase vocoder in the language of analysis?

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That Wikipedia article is bad in that it spends half the time talking about the phase coherence problem, never explaining the frequency domain manipulations. I think this site goes into an ok level of detail. Look at the "Processing" section. guitarpitchshifter.com/algorithm.html Your best bet is probably to find a good implementation and pick it apart. –  dls Jul 30 '13 at 22:44
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