A novel double-decomposition method for systolic implementation of DFT

Abstract

The authors discuss a novel systolic implementation of the discrete Fourier transform (DFT) algorithm by using a novel double-decomposition method to create two 4-point systolic preprocessors for a direct linear DFT implementation. The approach is well suited for large DFTs and reduces the number of required processors very effectively. The decomposition is carried out in two phases, first in the frequency and then in the time domain. With this double-decomposition, an N-point DFT can be implemented using sixteen N/16-point DFTs. A corresponding fully pipelined word-level systolic implementation is developed with time complexity O(N), in which only N/16+4 systolic processors are used in addition to 24 complex adders, three real adders, and five real multipliers. The elements of the systolic processors are of CORDIC (coordinate rotation digital computer)-type. >