Gabor analysis over finite Abelian groups

Details Gabor analysis over finite Abelian groups Gabor analysis over finite Abelian groups

2007-03-08

arxiv.org/abs/math/0703228v2

Mathematics

Group Theory

Revised version: two new sections added, many typos fixed

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Gabor analysis over finite Abelian groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gabor analysis over finite Abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gabor analysis over finite Abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-642794