Characterization of rational time-frequency multi-window Gabor frames and their duals

Yan Zhang; Yun-Zhang Li

doi:10.4134/JKMS.2014.51.5.897

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

QR
Code

Article

HOME

ALL ARTICLES

View

J. Korean Math. Soc. 2014; 51(5): 897-918

Printed September 1, 2014

https://doi.org/10.4134/JKMS.2014.51.5.897

Characterization of rational time-frequency multi-window Gabor frames and their duals

Yan Zhang and Yun-Zhang Li

Beifang University of Nationalities, Beijing University of Technology

Abstract

Go to

Abstract

This paper addresses multi-window Gabor frames with rational time-frequency product. Such issue was considered by Zibulski and Zeevi (Appl. Comput. Harmonic Anal. 4 (1997), 188--221) in terms of Zak transform matrix (so-called Zibuski-Zeevi matrix), and by many others. In this paper, we introduce of a new Zak transform matrix. It is different from Zibulski-Zeevi matrix, but more direct and convenient for our purpose. Using such Zak transform matrix we characterize rational time-frequency multi-window Gabor frames (Riesz bases and orthonormal bases), and Gabor duals for a Gabor frame. Some examples are also provided, which show that our Zak transform matrix method is efficient.

Keywords: frame, Gabor frame, multi-window Gabor frame

MSC numbers: 42C15, 42C40