Time-domain characterization of multiwindow Gabor systems on discrete periodic sets

Qiao-Fang Lian (), Jing Gong () and Ming-Hou You ()
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Qiao-Fang Lian: Beijing Jiaotong University
Jing Gong: Beijing Jiaotong University
Ming-Hou You: The Pilot College of Beijing University of Techology

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 1, 47-76

Abstract: Abstract This paper addresses multiwindow Gabor systems on discrete periodic sets, which can model signals to appear periodically but intermittently. We give some necessary and/or sufficient conditions for multiwindow Gabor systems to foe frames on discrete periodic sets, and characterize two multiwindow Gabor Bessel sequences to foe dual frames on discrete periodic sets. For a given multiwindow Gabor frame, we derive all its Gabor duals, among which we obtain an explicit expression of the canonical Gabor dual. In addition, we generalize multiwindow Gabor systems to the case of a different sampling rate for each window, and investigate multiwindow Gabor frames and dual frames in this case. We also show the properties of the multiwindow Gabor systems are essentially not changed by replacing the exponential kernel with other kernels.

Keywords: Gabor system; multiwindow Gabor frame; Gabor dual; periodic set (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0003-1

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