Gabor analysis over finite Abelian groups
By Hans G. Feichtinger, Werner Kozek, Franz Luef. 2007
70 citations recorded by the source corpus.
Abstract Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time–frequency plane, are the central topic of this paper. Our generic approach covers both multi-dimensional signals as well as non-separable lattices, and in fact the multi-window case as well. Our generic approach includes most of the 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 and others. In our presentation the spreading representation of linear operators between finite-dimensional Hilbert space as well as a symplectic version of Poisson's summation formula over the finite time–frequency plane are essential ingredients. They bring us to the so-called 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 discussed in this paper 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, independent of the structure theory theorem for finite Abelian groups.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing
View Paper: https://www.semanticscholar.org/paper/7899884f26efd8434c9b848de0f25da1386469a2
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In Applied Mathematics
In Computer Vision and Pattern Recognition
In Signal Processing
Citations in the corpus
- Gabor Frames in Finite Dimensions (2013, background): “(It is, in fact, up to isomorphisms, the only irreducible faithful projective representation of G× Ĝ on CG [34].”