Simplified addressing scheme for mixed radix FFT algorithms

Abstract

A mixed radix algorithm for the in-place fast Fourier transform (FFT), which is broadly used in most embedded signal processing fields, can be explicitly expressed by an iterative equation based on the Cooley-Tukey algorithm. The expression can be applied to either decimation-in-time (DIT) or decimation-in-frequency (DIF) FFTs with ordered inputs. For many newly emerging low power portable computing applications, such as mobile high definition video compressing, mobile fast and accurate satellite location, etc., the existing methods perform either resource consuming or non-flexible. In this paper, we propose a new addressing scheme for efficiently implementing mixed radix FFTs. In this scheme, we elaborately design an accumulator that can generate accessing addresses for the operands, as well as the twiddle factors. The analytical results show that the proposed scheme reduces the algorithm complexity meanwhile helps the designer to efficiently choose an arbitrary FFT to design the in-place architecture.