Row-column algorithms for the evaluation of multidimensional DFT´S on arbitrary periodic smapling lattices

Recent work by Mersereau and Speake [1,2] has shown that multidimensional discrete Fourier transforms (DFTs) can be defined for signals defined on any periodic sampling lattice and that they can be evaluated using a generalization of the Cooley-Tukey FFT algorithm. The main purpose of this work was to develop alternative algorithms which were more suitable to highly parallel machine architectures and which required less data handling than the Cooley-Tukey algorithms. Such an algorithm is described here. It makes use of the Smith normal form representation of an integer matrix. As a sidelight to this work a Chinese remainder theorem for lattices has been developed which permits an extension of Good´s prime factor algorithm. This is also described.