Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2013.04.16
  • Published : 2014.09.01
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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

References

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