Multidimensional nonseparable Gabor expansions

Werner Kozek; Hans Georg Feichtinger; Peter Prinz; Thomas Strohmer

doi:10.1117/12.255227

23 October 1996 Multidimensional nonseparable Gabor expansions

Werner Kozek, Hans Georg Feichtinger, Peter Prinz, Thomas Strohmer

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255227
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

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, and Thomas Strohmer "Multidimensional nonseparable Gabor expansions", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255227

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