Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/35271
Title: | Gabor orthonormal bases, tiling and periodicity |
Author: | Pinos, Alberto Debernardi Lev, Nir |
Issue Date: | 2022 |
Publisher: | Springer |
Abstract: | We show that if the Gabor system $\{g(x − t)e^{2\pi isx}, t\in T,s\in S\}$, is an orthonormal basis in $L^2(\mathbb{R})$ and if the window function $g$ is compactly supported, then both the time shift set $T$ and the frequency shift set $S$ must be periodic. To prove this we establish a necessary functional tiling type condition for Gabor orthonormal bases which may be of independent interest. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/35271 |
DOI: | 10.1007/s00208-021-02324-1 |
ISSN: | 0025-5831 |
Publisher Version: | https://link.springer.com/content/pdf/10.1007/s00208-021-02324-1.pdf |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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2022 A. Debernardi Pinos and N. Lev, Gabor orthonormal bases, tiling and periodicity.pdf | 243.09 kB | Adobe PDF | View/Open |
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