An enhanced model for software realisation of recursive prime radix discrete Fourier transform

Abstract

An enhanced model is proposed for a software realization of the recursive prime radix algorithms used for computing the discrete Fourier transform. It is shown that a very efficient in-place, in-order prime factor mapping (PFM) addressing scheme can best be applied to the model. In this scheme, a single mapping equation is used for both data loading and data retrieval, hence no extra unscrambling process is required. The authors propose the use of a form of two parallel recursive digital filters for the computation of each short-length DFT (discrete Fourier transform). A significant improvement in speed is thereby achieved. This algorithm has been realized using Fortran 77 language with the IBM PC AT. Results of the realization show that the proposed software computation model can achieve a 44% speed improvement over the radix-2 FFT (fast Fourier transform) algorithm, whereas the code length is comparable. As compared with the prime factor algorithm, it has a similar, if not better, speed performance for medium-length DFT computations. However, the code length is much shorter. This approach has the advantage of a large choice of sequence lengths, unlike the FFT algorithms. >