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This paper addresses multi-window Gabor frames with ratio- nal 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 oth- ers. 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 orthonor- mal bases), and Gabor duals for a Gabor frame. Some examples are also provided, which show that our Zak transform matrix method is efficient.
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참고문헌 (21)
참고문헌 신청
A. Ron / 1997 / Affine systems in L2(Rd) : the analysis of the analysis operator / J. Funct. Anal 148 (2) : 408 ~ 447
C. Heil / 2007 / History and evolution of the density theorem for Gabor frames / J. Fourier Anal. Appl 13 (2) : 113 ~ 166
F. Jaillet / 2007 / Time-frequency jigsaw puzzle: adaptive multiwindow and multilayered Gabor expansions / Int. J. Wavelets Multiresolut. Inf. Process 5 (2) : 293 ~ 315
H. G. Feichtinger / 1998 / Gabor Analysis and Algorithms, Theory and Applications / Birkhauser
H. G. Feichtinger / 2003 / Advances in Gabor Analysis / Birkhauser
C. Heil / 2007 / History and evolution of the density theorem for Gabor frames / J. Fourier Anal. Appl 13 (2) : 113 ~ 166
F. Jaillet / 2007 / Time-frequency jigsaw puzzle: adaptive multiwindow and multilayered Gabor expansions / Int. J. Wavelets Multiresolut. Inf. Process 5 (2) : 293 ~ 315
H. G. Feichtinger / 1998 / Gabor Analysis and Algorithms, Theory and Applications / Birkhauser
H. G. Feichtinger / 2003 / Advances in Gabor Analysis / Birkhauser
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