Some counterexamples in the theory of Weyl-Heisenberg frames

A Necessary Condition for Weyl-Heisenberg Frames

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

Tight Weyl-Heisenberg frames in l2(Z)

Tight Weyl–Heisenberg frames in `(Z) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short-time Fourier analysis in the joint time–frequency plane is not attainable unless some redundancy is introduced. That is the reason for consideri...

A Discrete Zak Transform

A discrete version of the Zak transform is defined and used to analyze discrete Weyl–Heisenberg frames, which are nonorthogonal systems in the space of square-summable sequences that, although not necessarily bases, provide representations of square-summable sequences as sums of the frame elements. While the general theory is essentially similar to the continuous case, major differences occur w...

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...

Frames in rotated time-frequency planes

Weyl-Heisenberg frames are complete signal representations corresponding to rectangular tiling of the time-frequency plane. Extensions of these frames are obtained in the rotated time-frequency planes by using the fractional Fourier transformation. It is shown that rotation does not affect the frame bounds. For some specific angles, lattices in rotated coordinates will map to the lattices in th...