A Generalized Prime Factor FFT Algorithm for any N = 2p 3q 5r

Prime factor fast Fourier transform (FFT) algorithms have two important advantages: they can be simultaneously self-sorting and in-place, and they have a lower operation count than conventional FFT algorithms. The major disadvantage of the prime factor FFT has been that it was only applicable to a limited set of values of the transform length N. This paper presents a generalized prime factor FFT, which is applicable for any N 2P3q5 r, while maintaining both the self-sorting in-place capability and the lower operation count. Timing experiments on the Cray Y-MP demonstrate the advantages of the new algorithm. Key words, fast Fourier transform (FFT), prime factor algorithm (PFA), self-sorting FFT, in-place FFT AMS(MOS) subject classification. 65T05