Some constructions of Gabor K-frames

Hamid Faraj, Mohamed Maghfoul, Samir Kabbaj

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.

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Published: 2021-12-21

How to Cite this Article:

Hamid Faraj, Mohamed Maghfoul, Samir Kabbaj, Some constructions of Gabor K-frames, J. Math. Comput. Sci., 12 (2022), Article ID 39

Copyright © 2022 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.

 

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