A self-sorting in-place fast Fouriertransform algorithm suitable for vector and parallelprocessing

Abstract

We propose a new algorithm for fast Fourier transforms. Thisalgorithm features uniformly long vector lengths and stride onedata access. Thus it is well adapted to modern vectorcomputers like the Fujitsu VP2200 having several floating pointpipelines per CPU and very fast stride one data access. It alsohas favorable properties for distributed memory computers asall communication is gathered together in one step. Thealgorithm has been implemented on the Fujitsu VP2200 using thebasic subroutines for fast Fourier transforms discussedelsewhere.We develop the theory of index digit permutations to someextent. With this theory we can derive the splitting formulasfor almost all mixed-radix FFT algorithms known so far. Thisframework enables us to prove these algorithms but also toderive our new algorithm. The development and systematic use ofthis framework is new and allows us to simplify theproofs which are now reduced to the application of matrixrecursions. © 1994, Springer-Verlag Berlin Heidelberg. All rights reserved.