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Recent work, apparently beginning with a paper by Welch in 1966, has shown that character expansions on finite Abelian groups can be fast computed in a way that makes the FFT and FWT special cases. It is shown here how the computational saving depends on the annihilator subgroup of the character group under consideration.
Abstract harmonic analysis, digital filtering, fast Fourier transform, Fourier analysis, time series processing.
T.W. Cairns, "On the Fast Fourier Transform on Finite Abelian Groups", IEEE Transactions on Computers, vol. 20, no. , pp. 569-571, May 1971, doi:10.1109/T-C.1971.223291
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