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

Ole Christensen, H. O. Kim, Kim Rae Young

    Research output: Contribution to journalJournal articleResearchpeer-review

    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.
    Original languageEnglish
    JournalApplied and Computational Harmonic Analysis
    Volume28
    Issue number1
    Pages (from-to)89-103
    ISSN1063-5203
    DOIs
    Publication statusPublished - 2010

    Keywords

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

    Cite this