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

Ole Christensen, Hong Oh Kim, Rae Young Kim

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    Abstract

    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
    Volume36
    Issue number4
    Pages (from-to)525-545
    ISSN1019-7168
    DOIs
    Publication statusPublished - 2012

    Keywords

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

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