Gabor analysis over finite Abelian groups
| dc.creator | Feichtinger, H. G. | |
| dc.creator | Kozek, W. | |
| dc.creator | Luef, F. | |
| dc.date | 2007-03-08 | |
| dc.date | 2008-03-17 | |
| dc.date.accessioned | 2026-07-07T09:26:56Z | |
| dc.date.available | 2026-07-07T09:26:56Z | |
| dc.description | The topic of this paper are (multi-window) Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time-frequency plane. Our generic approach covers simultaneously multi-dimensional signals as well as non-separable lattices. The main results reduce to well-known fundamental facts about Gabor expansions of finite signals for the case of product lattices, as they have been given by Qiu, Wexler-Raz or Tolimieri-Orr, Bastiaans and Van-Leest, among others. In our presentation a central role is given to spreading function of linear operators between finite-dimensional Hilbert spaces. Another relevant tool is a symplectic version of Poisson's summation formula over the finite time-frequency plane. It provides the Fundamental Identity of Gabor Analysis.In addition we highlight projective representations of the time-frequency plane and its subgroups and explain the natural connection to twisted group algebras. In the finite-dimensional setting these twisted group algebras are just matrix algebras and their structure provides the algebraic framework for the study of the deeper properties of finite-dimensional Gabor frames. | |
| dc.description | Revised version: two new sections added, many typos fixed | |
| dc.identifier | https://arxiv.org/abs/math/0703228 | |
| dc.identifier | http://arxiv.org/abs/math/0703228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156929 | |
| dc.subject | Group Theory | |
| dc.title | Gabor analysis over finite Abelian groups | |
| dc.type | text |