A new prime factor FFT algorithm

This paper presents an approach to calculating the discrete Fourier transform (DFT) using a prime factor algorithm (PFA). A very simple indexing scheme is employed that results in a flexible, modular program that very efficiently calculates the DFT in-place. A modification of this indexing scheme gives a new algorithm with the output both in-place and in-order at a slight cost in flexibility. This means only 2N data storage is needed for a length N complex FFT and no unscrambling is necessary. The basic part of a FORTRAN program is given. A speed comparison shows the new algorithm to be faster than both the Cooley-Tukey and the nested Winograd algorithms.