The fast fourier transform commonly abbreviated as fft is a fast algorithm for computing the discrete fourier transform of a sequence the purpose of this project is to investigate some of the mathematics behind the fft as well as the closely related discrete sine and cosine transforms i will produce a small library of matlab code which implements the algorithms discussed and i will also . Chapter 6 gives a discussion of the computational algorithms that have come to be known collectively as the fast fourier transform fft decimation in time and decimation in frequency are covered the discrete fourier transform is introduced and its properties are examined the applications of the fft are discussed in relation to spectral analysis fast convolution fast correlation and . Summary this chapter contains sections titled discrete fourier transform fast fourier transforms applications implementation considerations experiments using the tms320c55x references exercises. Of the fast fourier transform algorithm had been pub lished many years ago by runge and konig 10 and by stumpff 12 13 these are authors whose works are widelyread andtheir paperscertainly were used by those computing fourier series howthen could these importantalgorithms havegoneunnoticed theanswer is that the papers of runge k6nig and stumpif de scribed primarily how one could use