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An algorithm for computing the mixed radix fast Fourier transform

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1 Author(s)
Singleton, Richard C. ; Stanford Research Institute, Menlo Park, CA, USA

This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimension n of the transform is factored (if possible), and n/p elementary transforms of dimension p are computed for each factor p of n . An improved method of computing a transform step corresponding to an odd factor of n is given; with this method, the number of complex multiplications for an elementary transform of dimension p is reduced from (p-1)^{2} to (p-1)^{2}/4 for odd p . The fast Fourier transform, when computed in place, requires a final permutation step to arrange the results in normal order. This algorithm includes an efficient method for permuting the results in place. The algorithm is described mathematically and illustrated by a FORTRAN subroutine.

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Audio and Electroacoustics, IEEE Transactions on  (Volume:17 ,  Issue: 2 )