Scalable Parallel Algorithms for Multidimensional Digital Signal Processing

A new algorithm for the multiprocessor computation of the multidimensional discrete Fourier transform is presented. The algorithm eliminates the need for interprocessor communication and is highly scalable. The cost of eliminating interprocessor communication by this method is that one addition must be performed at each processing element for every input loaded into the machine. The algorithm is based on a new multidimensional discrete Fourier transform algorithm that computes a d-dimensional discrete Fourier transform by a set of independent k-dimensional discrete Fourier transforms kd it is a reduction algorithm in the sense that it has lowered the dimension of the Fourier transforms that are computed. The k-dimensional discrete Fourier transforms are performed on data derived from the input using only additions, and produce k-dimensional hyperplanes of the output array. Multidimensional discrete fourier transform algorithms, Parallel algorithms.