Abstract
Fourier transform algorithms are described using tensor (Kronecker) products and an associated class of permutations. Algebraic properties of tensor products and the related permutations are used to derive variants of the Cooley-Tukey fast Fourier transform algorithm. These algorithms can be implemented by translating tensor products and permutations to programming constructs. An implementation can be matched to a specific computer architecture by selecting the appropriate variant. This methodology is carried out for the Cray X-MP and the AT&T DSP32.
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