Fast algorithms for the multidimensional discrete Fourier transform

In this paper, the prime factor algorithm for the evaluation of a one-dimensional discrete Fourier transform is generalized to the evaluation of multidimensional discrete Fourier transforms defined on arbitrary periodic sampling lattices. It is shown that such an algorithm is equivalent in computational complexity to the evaluation of a rectangular discrete Fourier transform. As a sidelight to the derivation of the algorithm, a Chinese remainder theorem is derived for integer lattices.