The Duality Condition for Weyl-heisenberg Frames

A Necessary Condition for Weyl-Heisenberg Frames

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Oversampled Wilson Expansions - IEEE Signal Processing Letters

Recently orthonormal Wilson bases with good time–frequency localization have been constructed by Daubechies, Jaffard, and Journé. We extend this construction to Wilson sets and frames with arbitrary oversampling (or redundancy). We state conditions under which dual Weyl–Heisenberg (WH) sets induce dual Wilson sets, and we formulate duality conditions in the time domain and frequency domain. We ...

Plancherel transform criteria for Weyl-Heisenberg frames with integer oversampling

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 regard to the action of a suitably defined type-I discrete group G. This allows to relate the construction of Weyl-Heisenber...

An Introduction to Irregular Weyl-Heisenberg Frames

We give an introduction to irregular Weyl-Heisenberg frames showing the latest developments and open problems. We provide several new results for semiirregular WH-frames as well as giving new and more accessable proofs for several results from the literature.