<title>Fourier Transform Faster Than Fast Fourier Transform (FFT)</title>

Abstract

AbstractBecause of the rapid advances in multiplication hardware, the most time consuming processing step inFourier Transform will be the number of memory accesses rather than the number of multiplications. Analgorithm of Continuous Fourier Transform (CFT) which minimizes memory access was developed. It can beimplemented with existing technology and is potentially faster than FFT, particularly for processing continuous, real -time signals. IntroductionSince its publication by Cooley and Tukey,l Fast Fourier Transform (FFT) has been the principal techniqueemployed in the computer realization of Fourier analysis for most applications. The success of FFT lies inthe fact that the number of multiplications, which until very recently has been the most time consumingoperation in the computation, is minimized to the order to N log2N from N2, where N is the number of datavalues to be transformed.As indicated by recent advancements in the LSI and computer technologies, multiplications can be done asfast as additions,2'3 and low cost CPU's can be ganged together in parallel to increase processing throughput.These developments point to new directions of signal processing which might achieve even greater throughputthan the FFT as implemented on a single CPU computer. Here I shall outline the theoretical justificationsof such a design and suggest ways of its hardware implementation with currently available LSI technology.This type of Fourier Transform processor is capable of processing signals sampled at a rate in excess of