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

Publication: Research - peer-reviewJournal article – Annual report year: 2010

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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.
Original languageEnglish
JournalApplied and Computational Harmonic Analysis
Publication date2010
Volume28
Issue1
Pages89-103
ISSN1063-5203
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 5

Keywords

  • Dual frame, Dual window, Gabor frame, Gabor system
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