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http://dx.doi.org/10.4134/JKMS.2014.51.5.897

CHARACTERIZATION OF RATIONAL TIME-FREQUENCY MULTI-WINDOW GABOR FRAMES AND THEIR DUALS  

Zhang, Yan (School of Mathematics and Information Science Beifang University of Nationalities)
Li, Yun-Zhang (College of Applied Sciences Beijing University of Technology)
Publication Information
Journal of the Korean Mathematical Society / v.51, no.5, 2014 , pp. 897-918 More about this Journal
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;
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