A parallel algorithm for 2-D DFT computation with no interprocessor communication

Abstract

A parallel algorithm is proposed for the two-dimensional discrete Fourier transform (2-D DFT) computation which eliminates interprocessor communications and uses only O(N) processors. The mapping of the algorithm onto architectures with broadcast and report capabilities is discussed. Expressions are obtained for estimating the speed performance on these machines as a function of the size N*N of the 2-D DFT, the bandwidth of the communications channel, the time for an addition, the time T(F/sub N/) for a single processing element to perform an N-point DFT, and the degree of parallelism. For single I/O channel machines that are capable of exploiting the full degree of parallelism of the algorithm, attainable execution times are as low as the time T(F/sub N/) plus the I/O time for data upload and download. An implementation on a binary tree computer is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>