Some constructions of Gabor K-frames
Abstract
It is known that a necessary condition for Gabor systems {EmbTnag}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 {Emb/qTna/pg}m,n∈Z of a K-frame {EmbTnag}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.
Copyright © 2021 Hamid Faraj, Mohamed Maghfoul, Samir Kabbaj. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
H. Faraj, M. Maghfoul, S. Kabbaj, Some constructions of Gabor K-frames, J. Math. Comput. Sci. 12 (2022), 39. https://doi.org/10.28919/jmcs/6821
BibTeX
@article{Faraj2022,
author = {Faraj, Hamid and Maghfoul, Mohamed and Kabbaj, Samir},
title = {Some constructions of Gabor K-frames},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {39},
doi = {10.28919/jmcs/6821}
}