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I've read that sparse fast Fourier transform can be used to compute the Fourier transform of a signal that is sparse in frequency domain much faster compared to FFT. My question is that can SFFT be used for signal that is not sparse in frequency domain but in some other domains?

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No.

What did you expect? For sparse algorithm to work, the signal has to be sparse. If it's sparse after a integral transform, that doesn't mean it's sparse under a different transform.

Also note that according to this answer, the benefit of the sparse fft only apply to very sparse signals - a factor of at least about 2000 between the zero and non-zero bins.

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