A general scrambling rule for multidimensional FFT algorithms

This work determines the scrambling rule of the multidimensional Cooley-Tukey FFT, and of the multidimensional prime factor FFT, in complete generality, i.e., for signals defined on lattices of general type. The characteristics of the scrambling rule bear interesting similarities with the 1-D case: the scrambling can be performed on the input data and it can be eliminated from the operations requiring pairs of FFT and inverse FFT (e.g. convolutions and correlations). The results of this work allow one to derive the most efficient way of performing multidimensional scrambling. The consequent memory access savings are relevant, especially with arrays of sizable dimensions