A class of orthogonal refinable functions and wavelets

Timothy Goodman

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    8 Citations (Scopus)


    We give a construction, for any n 2, of a space S of spline functions of degree n – 1 with simple knots in (1/4)Z which is generated by a triple of refinable, orthogonal functions with compact support. Indeed, the result holds more generally by replacing the B-spline of degree n – 1 with simple knots at the integers by any continuous refinable function whose mask is a Hurwitz polynomial of degree n. A simple construction is also given for the corresponding wavelets.
    Original languageEnglish
    Pages (from-to)525-540
    Number of pages16
    JournalConstructive Approximation
    Issue number4
    Publication statusPublished - 2003



    • Wavelet
    • Multiwavelet
    • B-spline
    • Orthogonal

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