Gabor windows supported on [-1,1] and compactly supported dual windows

Title
Gabor windows supported on [-1,1] and compactly supported dual windows
Author(s)
김래영Ole Christensen[Ole Christensen]김홍오[김홍오]
Keywords
FRAMES; BASES
Issue Date
201001
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, v.28, no.1, pp.89 - 103
Abstract
Consider a bounded function g supported on [-1, 1] and a modulation parameter b is an element of inverted left perpendicular1/2, 1inverted right perpendicular for which the Gabor system {E(mb)T(n)g}(m,n is an element of Z) is a frame. We show that such a frame always has a compactly supported dual window. More precisely, we show that if b < N/N+1 for some N is an element of N, it is possible to find a dual window supported on [-N, N]. Under the additional assumption that g is continuous and only has a finite number of zeros on inverted left perpendicular-1, 1inverted right perpendicular, we characterize the frame property of {E(mb)T(n)g}(m,n is an element of Z). As a consequence we obtain easily verifiable criteria for a function g to generate a Gabor frame with a dual window having compact support of prescribed size. (C) 2009 Elsevier Inc. All rights reserved.
URI
http://hdl.handle.net/YU.REPOSITORY/23026http://dx.doi.org/10.1016/j.acha.2009.07.004
ISSN
1063-5203
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이과대학 > 수학과 > Articles
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