Twiddle factor transformation for pipelined FFT processing

Abstract

This paper presents a novel transformation technique that can derive various fast Fourier transform (FFT) in a unified paradigm. The proposed algorithm is to find a common twiddle factor at the input side of a butterfly and migrate it to the output side. Starting from the radix-2 FFT algorithm, the proposed common factor migration technique can generate most of previous FFT algorithms without using mathematical manipulation. In addition, we propose new FFT algorithms derived by applying the proposed twiddle factor moving technique, which reduce the number of twiddle factors significantly compared with the previous algorithms being widely used for pipelined FFT processing.