Original scientific paper

A note on Gabor frames

Shiv Kumar Kaushik orcid.org/0000-0002-2850-0432 ; Department of Mathematics, Kirorimal College, University of Delhi, Delhi, India
Suman Panwar ; Department of Mathematics, University of Delhi, Delhi, India

Abstract

Wilson frames $\{\psi_j^k :w_0,w_{-1}\in
L^2(\mathbb{R})\}_{j\in\mathbb{Z}\atop {k \in\mathbb{N}_0}}$ in
$L^2(\mathbb{R})$ have been defined and a characterization of Wilson frames in terms of Gabor frames is given when $w_0=w_{-1}$. Also, under certain conditions a necessary condition for a Wilson system to be a Wilson Bessel sequence is given. We have also obtained sufficient conditions for a Wilson system to be a Wilson frame in terms of Gabor Bessel sequences. For $w_0=w_{-1}$, stability of Wilson frames is discussed. Also, under the same assumption a necessary and sufficient condition is given for a Wilson system to be a Wilson Bessel sequence in terms of a Wilson frame.

Keywords

Gabor frames; Wilson frames; Gabor Bessel sequence; Wilson Bessel sequence

Hrčak ID:

121827

URI

https://hrcak.srce.hr/121827

Publication date:

26.5.2014.

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