Recursive Fast Fourier Transforms

Abstract

The development of the Fast Fourier Transform in complex notation has obscured the savings that can be made through the use of recursive properties of trigometric functions. A disadvantage of the Fast Fourier Transform is that all samples of the function must be stored in memory before processing can start. The computation in the Fast Fourier Transform occurs after the receipt of the last sample of the function; there is no processing of the incoming data prior to this point. Thus if there are N samples of each function, and G different functions (in G "gates" or "channels"), then a total of GN words must be stored in memory.