Under-sampled Weyl–Heisenberg expansions via orthogonal projections in Zak space

Abstract An algorithm is presented which orthogonally projects signals into integer under-sampled Weyl–Heisenberg subspaces. The algorithm operates by periodization–decimation operations in Zak space, and can be viewed as direct Zak space extension of classical signal space procedures underlying orthogonal projections of Fourier expansions, the basis of divide and conquer fast Fourier transform algorithms. The language of groups is used, which highlights the duality between time and frequency spaces and facilitates sampling rate conversion. Results of numerical experiments are included, suggesting that the algorithm can be used for arrival time estimation of a partially known signal.