Plancherel transform criteria for Weyl-Heisenberg frames with integer oversampling

Abstract

We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such Weyl-Heisenberg frames are admissible with respect to the action of suitably defined type-I discrete group G. This allows to relate the construction of Weyl-Heisenberg frames to the Plancherel measure of G, which provides an alternative proof and a new interpretation of the well-known Zak transform based criterion for tight Weyl-Heisenberg frames with integer oversampling.