Irregular Gabor frames of Cauchy kernels

TL;DR

This paper investigates the conditions under which Gabor systems generated by a Cauchy kernel on irregular lattices form frames, contributing to the understanding of time-frequency analysis with non-uniform sampling.

Contribution

It provides new insights into the frame properties of Gabor systems with Cauchy kernels on irregular lattices, a less explored area in time-frequency analysis.

Findings

Established criteria for Gabor frames with Cauchy kernels on irregular lattices

Extended frame theory to non-uniform sampling scenarios

Identified conditions ensuring stable signal representations

Abstract

We study the frame property of the Gabor system corresponding to an irregular lattice with a single Cauchy kernel as the generating window.