Constructing pairs of dual bandlimited frame wavelets in L^2(R^n)

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    Abstract

    Given a real, expansive dilation matrix we prove that any bandlimited function ψ∈L2(Rn), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose generators have compact support in the Fourier domain and desired time localization. The construction relies on a technical condition on ψ, and we exhibit a general class of function satisfying this condition.
    Original languageEnglish
    JournalApplied and Computational Harmonic Analysis
    Volume32
    Issue number3
    Pages (from-to)313-328
    ISSN1063-5203
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Dual wavelet frames
    • Bandlimited wavelets
    • Real dilation matrix
    • Partition of unity
    • Non-tight frames

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