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연구기관
수리과학연구소
Journal papers
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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
SCOPUS Author ID
장수미
Issue Date
2013
Journal Title
Advances in Computational Mathematics
ISSN
1019-7168
Citation
Advances in Computational Mathematics vol. 38, no. 1, pp. 159 - 186
Indexed
SCIE; SCOPUS
Document Type
Article
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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