Multidimensional fast Fourier transform algorithm for signals with arbitrary symmetries

Abstract

A multidimensional fast Fourier transform (FFT) algorithm is presented for signals with arbitrary symmetries and periodic on arbitrary lattices. Applications that can benefit from such an algorithm include Volterra filtering and analysis of x-ray diffraction data. The presented algorithm exploits signal redundancy to achieve a computational complexity of N log N, where N is the number of independent samples. To the authors’ knowledge, this is the only FFT that makes the frequency domain computation of Volterra filtering more convenient than the time domain approach.