Plancherel transform criteria for Weyl-Heisenberg frames with integer oversampling

Details Plancherel transform criteria for Weyl-Heisenberg frames with integer oversampling Plancherel transform criteria for Weyl-Heisenberg frames with integer oversampling

2002-06-28

arxiv.org/abs/math/0206309v1

Mathematics

Functional Analysis

13 pages

Scientific paper

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.

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