Factorization of Fourier and Laplace transforms as a basis of the fast Fourier transform
J.E. Carroll · International Journal of Electronics · 1975
A mechanistic method of finding the next step in an arbitrarily large fast Fourier transform at an arbitrary stage is outlined. The method starts by writing down two different forms for the discrete Fourier transform of a sampled function and converting one into the other by decomposition using partial fractions. The process demonstrated corresponds to decimation in time. The alternative of decimation in frequency is demonstrated through an analogous procedure using the Laplace transform of a sampled function. It is suggested that the method should help in understanding the organization of a large-scale FFT.