Symmetric, discrete fractional splines and Gabor systems

Peter Lempel Søndergaard

    Research output: Book/ReportReportResearch

    Abstract

    In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases.
    Original languageEnglish
    Publication statusPublished - 2006
    SeriesMAT Preprints
    Number2007-01

    Keywords

    • Wilson bases
    • Fractional splines
    • Gabor systems
    • Hurwitz zeta function

    Cite this

    Søndergaard, P. L. (2006). Symmetric, discrete fractional splines and Gabor systems. MAT Preprints, No. 2007-01
    Søndergaard, Peter Lempel. / Symmetric, discrete fractional splines and Gabor systems. 2006. (MAT Preprints; No. 2007-01).
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    Søndergaard, PL 2006, Symmetric, discrete fractional splines and Gabor systems. MAT Preprints, no. 2007-01.

    Symmetric, discrete fractional splines and Gabor systems. / Søndergaard, Peter Lempel.

    2006. (MAT Preprints; No. 2007-01).

    Research output: Book/ReportReportResearch

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    AB - In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases.

    KW - Wilson bases

    KW - Fractional splines

    KW - Gabor systems

    KW - Hurwitz zeta function

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    Søndergaard PL. Symmetric, discrete fractional splines and Gabor systems. 2006. (MAT Preprints; No. 2007-01).