Pairs of dual periodic frames

Ole Christensen, Say Song Goh

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    Abstract

    The time–frequency analysis of a signal is often performed via a series expansion arising from well-localized building blocks. Typically, the building blocks are based on frames having either Gabor or wavelet structure. In order to calculate the coefficients in the series expansion, a dual frame is needed. The purpose of the present paper is to provide constructions of dual pairs of frames in the setting of the Hilbert space of periodic functions L2(0,2π). The frames constructed are given explicitly as trigonometric polynomials, which allows for an efficient calculation of the coefficients in the series expansions. The generality of the setup covers periodic frames of various types, including nonstationary wavelet systems, Gabor systems and certain hybrids of them.
    Original languageEnglish
    JournalApplied and Computational Harmonic Analysis
    Volume33
    Issue number3
    Pages (from-to)315-329
    ISSN1063-5203
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Periodic frames
    • Gabor frames
    • Wavelet frames
    • Dual pairs of frames
    • Trigonometric polynomials

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