A new parallel algorithm for the multidimensional Fourier transform processing

Tools are presented for the extension of the Cooley-Tukey (1965) and Pease (1968) fast Fourier transform algorithms to arbitrary dimensions in a compact Kroenecker product formulation. Several variations of the vector radix algorithm (VRA) are presented using this formulation, and an algorithm suitable for spatial concurrency is derived. The tools presented are the multidimensional stride and partitioning permutations together with the multidimensional lower-ordered transforms. The concepts of partitioning permutation and multidimensional perfect shuffle permutations are studied. The first enables one to apply a divide-and-conquer strategy used in Cooley-Tukey algorithms to multidimensions and the second defines algorithm data flow in a lattice.<>