Efficient Fast Fourier Transform Programs for Arbitary Factors with One Step Loop Unscrambling

This correspondence develops efficient fast Fourier transform (FFT) programs to transform arrays of dimension N, where N can be written as a power of two possibly multiplied by arbitrary factors. Two programs were developed which use radix-2 and radix-4 transformations for the binary factors. These programs call another subprogram to transform with respect to the arbitrary factors, if any. Since the sequential transformation is well known, the emphasis is on developing an efficient unscrambling procedure to follow the transformation.