Application of parallel version two-dimensional fast Fourier transform calculating algorithm with an analogue of the Cooley-Tukey algorithm

Abstract

Currently, two-dimensional fast Fourier transform (FFT) is widely used in digital signal processing. It is usually calculated using a combination of one-dimensional FFTs, first for each row, then for each column. In this case, the algorithm is easily adapted for parallel computing. The paper presents a method of parallelizing the algorithm for calculating a two-dimensional FFT using an analogue of the Cooley-Tukey algorithm, which requires fewer operations of complex addition and complex multiplication than the standard method. The main difficulty in parallelizing this algorithm is that the two-dimensional analogue of the Cooley-Tukey algorithm is iteratively performed in s passes with the size of the initial signal 2^s*2^s. Moreover, in each of s iterations, the entire set of used data is recalculated. Methods for solving this problem during parallelization are described in the case of implementing an algorithm in the C ++ programming language using OpenMP and MPI parallel computing libraries. The results of the numerical experiment are presented, in which it is shown that parallelization achieves an acceleration of computations up to 4 times in comparison with the standard method for calculating two-dimensional FFT.