Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gabor analysis over finite Abelian groups   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.

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex