Computing the Fast Fourier Transform on a Vector Computer

Two algorithms are presented for performing a Fast Fourier Transform on a vector computer and are compared on the Control Data Corporation STAR-100. The relative merits of the two algorithms are shown to depend upon whether only a few or many independent transforms are desired. A theorem is proved which shows that a set of independent transforms can be computed by performing a partial transformation on a single vector. The results of this theorem also apply to nonvector machines and have reduced the average time per transform by a factor of two on the CDC 6600 computer.