Parallel FFT algorithms using radix 4 butterfly computation on an eight-neighbor processor array

Abstract

Fast Fourier transform (FFT), which has wide and variety application areas, requires very high speed computation. Since parallel processing of FFT is very attractive for high speed FFT computation, many processor arrays and multiprocessor systems have been proposed with efficient FFT algorithms. As a result of the recent development of VLSI technology, several massively parallel computers have been implemented on commercial basis. The MasPar, which is one of the SIMD type massively parallel computers, consists of an eight-neighbor processor array.

This paper discusses parallel 1-D FFT algorithms on an eight-neighbor processor array. We propose three algorithms according to various data allocation methods. Then we estimate and evaluate their processing time. With the number of processors N = N_r × N_r, processing time is estimated to be 2(N_r − 2)t_c + (log₂N_r)t_b, where t_c is the communication time between neighbor processors, and t_b is the execution time for the radix 4 butterfly computation. We also compare these algorithms with the conventional radix 2 FFT algorithm implemented on a mesh processor array. It is shown that the radix 4 FFT algorithms are faster than the radix 2 algorithms. These algorithms get high speed FFT computation by combining the radix 4 FFT algorithm with the characteristics of the eight-neighbor processor array.