Density of Gabor Frames

Ole Christensen, Christopher Heil, Baiqiao Deng

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    A Gabor system is a set of time-frequency shifts S(g, Lambda) = {e(2 pi ibx) g(x - a)}((a,b)is an element of Lambda) of a function g is an element of L-2(R-d). We prove that if a finite union of Gabor systems boolean (ORk=1S)-S-r(g(k), Lambda(k)) forms a frame for L-2(R-d) then the lower and upper Beurling densities of Lambda = boolean ORk=1r Lambda(k) satisfy D- (Lambda) greater than or equal to 1 and D+(Lambda) < infinity. This extends recent work of Ramanathan and Steger. Additionally, we prove the conjecture that no collection boolean ORk=1r {g(k)(x - a)}(a is an element of Gamma k) of pure translates can form a frame for L-2 (R-d). (C) 1999 Academic Press.
    Original languageEnglish
    JournalApplied and Computational Harmonic Analysis
    Volume7
    Issue number3
    Pages (from-to)292-304
    ISSN1063-5203
    DOIs
    Publication statusPublished - Nov 1999

    Keywords

    • Beurling density
    • frame
    • frame of translates
    • Gabor frame
    • Riesz basis

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