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Compactly supported multiwindow dual Gabor frames of rational sampling density

Title
Compactly supported multiwindow dual Gabor frames of rational sampling density
Authors
Jang S.Jeong B.Kim H.O.
Ewha Authors
장수미
Issue Date
2013
Journal Title
Advances in Computational Mathematics
ISSN
1019-7168JCR Link
Citation
vol. 38, no. 1, pp. 159 - 186
Indexed
SCIE; SCOPUS WOS scopus
Abstract
We consider multiwindow Gabor systems (GN; a, b) with N compactly supported windows and rational sampling density N/ab. We give another set of necessary and sufficient conditions for two multiwindow Gabor systems to form a pair of dual frames in addition to the Zibulski-Zeevi and Janssen conditions. Our conditions come from the back transform of Zibulski-Zeevi condition to the time domain but are more informative to construct window functions. For example, the masks satisfying unitary extension principle (UEP) condition generate a tight Gabor system when restricted on [0, 2] with a = 1 and b = 1. As another application, we show that a multiwindow Gabor system (GN; 1, 1) forms an orthonormal basis if and only if it has only one window (N = 1) which is a sum of characteristic functions whose supports 'essentially' form a Lebesgue measurable partition of the unit interval. Our criteria also provide a rich family of multiwindow dual Gabor frames and multiwindow tight Gabor frames for the particular choices of lattice parameters, number and support of the windows. (Section 4) © 2011 Springer Science+Business Media, LLC.
DOI
10.1007/s10444-011-9234-z
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연구기관 > 수리과학연구소 > Journal papers
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