Group-Theoretic Methods for Parallel Computation of Convolution

Abstract

Convolution decomposition allowed creation of fast computation algorithms within the scope of sequential processing [1], [2]. However, in one case, the de- composition methods made the algorithm structure redundant, whereas in other case, they imposed restrictions on the decomposition parameters, which need to be mutually prime numbers. Parallel processing requires structural flexibility of algorithms, therefore the decomposition methods primordially characterized by redundancy and restrictions imposed on the parameters are not effective. The methods oriented to parallel processing were created on the basis of the group- theoretic approach to decomposition. The approach is complex in character, that is, it is orientated towards the decomposition of a number of basic functions of digital signal processing — convolution, correlation, discrete Fourier transform (DFT). The objective of this paper is to develop a collection of methods for the parallel computation of convolution by generalizing and extending the results of the group-theoretic decomposition of DFT and convolution [3], [4].