Algorithms for defining mixed radix FFT flow graphs

A unified set of algorithms is presented to define the intraconnection and phase rotation structure of flow graphs for arbitrary fast Fourier transforms (FFTs). The same set of basic equations is applied to arbitrary-length FFTs; mixed-radix FFTs; either decimation-in-time or decimation-in-frequency FFTs; and FFTs with ordered inputs, ordered outputs, or both. These equations, which define input and output point indexing of each FFT stage and the twiddle factors used in each stage, are based on forward and backward products of radixes. The same basic products of radixes can be used to represent a wide variety of FFT structures. These equations also permit HOL (high-order language) specification of FFTs for programming signal processors