Recursive Zak transforms and Weyl-Heisenberg expansions

We develop algorithms for computing block-recursive Zak transforms and Weyl-Heisenberg expansions, which achieve p/logL and (logM+p)/(logN+logL+1) multiplicative complexity reduction, respectively, over direct computations, where p'=pM, and N-p' is the number of overlapping samples in subsequent signal segments. For each transform we offer a choice of two algorithms based on two different implementations of the Zak transform of the time-evolving signal. These two algorithm classes exhibit typical trade-offs between computational complexity and memory requirements.