Implementation of a self-sorting in-place prime factor FFT algorithm

Abstract A “prime factor” Fast Fourier Transform algorithm is described which is self-sorting and computes the transform in place. With a view to implementation on a Cray-1 or Cyber 205, the form of the algorithm is chosen to minimize the number of additions. With an appropriate choice of index mapping in the derivation, we obtain the unexpected result that the required indexing is actually simpler than that for a conventional FFT. The construction of the necessary “rotated” DFT modules is described, and comparisons are presented between the new algorithm and the conventional FFT in terms of operation counts and timings on an IBM 3081; on this machine, the new transform algorithm takes about 60% of the time for the conventional FFT. A Fortran routine for the new algorithm is outlined.

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