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

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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.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2010-01
Language
English
Article Type
Article
Keywords

FRAMES; BASES

Citation

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, v.28, no.1, pp.89 - 103

ISSN
1063-5203
DOI
10.1016/j.acha.2009.07.004
URI
http://hdl.handle.net/10203/96906
Appears in Collection
MA-Journal Papers(저널논문)
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