A new set of minimum-add small- n rotated DFT modules

Abstract

A self-sorting in-place prime factor FFT algorithm introduced in an earlier paper was based on a set of modules for performing small discrete Fourier transforms (DFTs) with an optional “rotation” of the results. The modules were designed to reduce the total number of additions in the FFT algorithm. In specializing this algorithm to the case of real or conjugate-symmetric input data, it was found necessary to redesign these modules to impose a particular structure. In some cases, the new modules proved to require fewer operations than the old. We describe the design procedure and compare the new operation counts with those for Winograd's DFT modules. The algorithms for the new modules are given in detail; these will be useful in coding FFT algorithms of either the “prime factor” or conventional variety.