23 October 1996 Multidimensional nonseparable Gabor expansions
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Abstract
Various generalizations of the classical Gabor expansion are considered. Studying the frame operator via the Kohn- Nirenberg correspondence allows to obtain straightforward structural results for the situation of (i) nonseparable prototypes, and/or (ii) nonseparable time-frequency sampling lattices, and/or (iii) multi-prototypes. For such general Weyl-Heisenberg frames, it is shown how to reformulate the Janssen representation of the frame operator and the Wexler- Raz result. Moreover, an analysis of the analysis operator is performed that leads to quantitative results about the variety of admissible analysis/synthesis prototypes.
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Werner Kozek, Hans Georg Feichtinger, Peter Prinz, Thomas Strohmer, "Multidimensional nonseparable Gabor expansions", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); doi: 10.1117/12.255227; https://doi.org/10.1117/12.255227
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