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I don't know as much as I would like to about Fourier analysis and I know almost nothing about wavelets. So just have a few conceptual questions to determine whether I should pursue their study or not. As I understand, the discrete fourier transform itself doesn't require points to be sampled uniformed in time, right? The time step in measuring the signal can be a variable. It is only when I want to use the fast fourier transform, I need the signal to be sampled uniformly. Is this correct? And what about wavelets? Does using the wavelet transform require uniform sampling too? Thanks!

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Not really an answer to your question, but you might find the NFFT interesting, which is a kind of FFT for Non-uniform samples - however, it is only approximative. –  cubic lettuce Nov 2 '12 at 9:10
Maybe you should ask the moderators to move this dsp.SE. –  Dilip Sarwate Nov 2 '12 at 18:48
I don't really know the answer to your question, but I can say that non-uniform sampling methods are pretty specialized. Chapter 13 of numerical recipes has a brief subsection on it, which might be worth reading (newer editions also talk about wavelets.) –  Bjorn Roche Nov 3 '12 at 15:34
I agree this is more a dsp.stackexchange.com question. By the way, as fas as I know, the discrete wavelet transform assumes uniform sampling. But sampling issues are general regardless of the transform. Why are you interested in wavelets? –  caya Feb 15 '13 at 2:33
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