Gabor windows supported on [ − 1, 1] and dual windows with small support

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Consider a continuous function g ∈ L 2(ℝ) that is supported on [ − 1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 for some N ∈ ℕ. Under an extra condition on the zeroset of the window g we show that there exists a continuous dual window supported on [ − N, N]. We also show that this result is optimal: indeed, if b2N2N+1 then a dual window supported on [ − N, N] does not exist. In the limit case b=2N2N+1 a dual window supported on [ − N, N] might exist, but cannot be continuous.
Original languageEnglish
JournalAdvances in Computational Mathematics
Publication date2012
Volume36
Issue4
Pages525-545
ISSN1019-7168
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 1

Keywords

  • Gabor frame, Compactly supported window, Compactly supported dual window
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