Some constructions of Gabor K-frames

Abstract

It is known that a necessary condition for Gabor systems {E_mbT_nag}_m,n∈Z to yield a frame is that ab≤1 (where a,b are the lattice parameters). In this paper we will characterize and construct Gabor (Weyl-Heisenberg) Kframes when ab > 1, and windows are in the Weiner algebra. We will show that an oversampling {E_mb/qT_na/pg}m,n∈Z of a K-frame {E_mbT_nag}_m,n∈Z is also a K-frame. Moreover, we will give a concrete example, in the case when g = χ_[0,1), a = 2, b = 1, and we will derive some results.