Fast n-D Fourier-Heisenberg-Weyl transforms

In this work we study the harmonic analysis of functions on the n-D Heisenberg groups H over the Galois field GF(p) for generating Gabor atoms. Analogous to the Fourier transform, the expansion of functions on the basis of irreducible complex matrix representations of the Heisenberg group defines the generalized Fourier transform on this group, or, simply, the Fourier-Heisenberg transform. The fast algorithms for the n-D Fourier transforms on the Heisenberg and affine groups are developed in this paper. A general method of computing the Gabor distribution and wavelet transform based on the fast Fourier-Heisenberg-Weyl transform is also presented.