Developing algorithms for multi-dimensional Fourier transforms, this book presents results that yield highly efficient code on a variety of vector and parallel computers. By emphasising the unified basis for the many approaches to both one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimising implementations. It will thus be of great interest not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers working on signal and image processing.

Tensor Product.- Multi-dimensional Tensor Product and FFT.- Finite Abelian Groups.- Fourier Transform of Finite Abelian Groups.- Cooley-Tukey and Good-Thomas.- Lines.- Duality of Lines and Planes.- Reduced Transform Algorithms.- Field Algorithm.- Implementation on Risc Architectures.- Implementation on Parallel Architectures.