Construction of Gabor frames in $l^2(\mathbb{Z})$ using Gabor frames in $L^2(\mathbb{R})$

Abstract

In this paper we identified a collection of unitary operators which maps Gabor frames in $L^2(\mathbb{R})$ to Gabor frames in $l^2(\mathbb{Z})$. This is very important in construction of Gabor frames in $l^2(\mathbb{Z})$ from Gabor frames in $L^2(\mathbb{R})$ other than which obtained from Gabor frames in $L^2(\mathbb{R})$ through sampling.