Fourier transform algorithm implementations on a general-purpose microprocessor

The Fourier representation of sequences plays a key roll in the analysis, the design, and the implementation of digital signal processing algorithms. The existence of very efficient algorithms for computing the Fourier transforms have expanded the importance of Fourier analysis in digital signal processing. To indicate the importance of efficient computational schemes, evaluation of two well-known algorithms - the Cooley-Tukey fast Fourier transform and complex general-N Winograd Fourier transform - were implemented on a general-purpose, high-speed, digital microprocessor - the MC68000. The Despain very fast Fourier algorithm was studied as well. Complexity measures for Fourier transforms, or the relative executional time of an implemented algorithm, have generally been based on the number of multiplications and additions required. For this reason, algorithmic improvements have primarily consisted of reduction in the number of multiplications and additions. However, large amounts of accessing and storing of data, as well as loop control overhead, are inherent in the implementation of these algorithms. Comparisons of the three algorithms as well as numerical versus data transfer operations are presented for a specific microprocessor implementation.