The structure of vector radix fast Fourier transforms

Abstract

A general form of the matrix representation for multidimensional, vector-radix, fast Fourier transform (FFT) algorithms using decimation-in-frequency is presented. A structure theorem is devised to construct systematically various vector-radix decimation-in-frequency FFT algorithms from their 1-D counterparts. Logic diagrams are provided to facilitate the software and hardware implementation of the algorithms. The computational complexity of several of the algorithms is considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>