Phases for dyadic orthonormal wavelets

    Authors

    Q. Gu;D. Q. Han

    Abbreviated Journal Title

    J. Math. Phys.

    Keywords

    Physics, Mathematical

    Abstract

    We consider real-valued functions alpha(s) and wavelets psiis an element ofL(2)(R) such that e(ialpha(s))\psi(s)\ is the Fourier transform of a wavelet. Such a function alpha(s) is called an attainable phase for the wavelet psi. It is known that for all multiresolution analysis (MRA) wavelets, the phase function alpha(s)=shape=1/2 s is attainable, and any real function alpha(s) is attainable by any minimally-supported-frequency (MSF) wavelet. Besides this, very little is known in the literature about attainable phases for wavelets. We study the problem of determining functions which are attainable phases for some (non-MSF) wavelets. We prove that there exists a non-MSF wavelet for which there is no attainable "set-wise" linear phase. This answers a basic question about wavelet phases. Although we do not know whether for any irrational number a, as is attainable by some non-MSF wavelets, we show that there exist certain rational numbers a such that as is not attainable by any non-MSF wavelet. We also prove that there exists a large class of rational numbers a such that as is attainable by some non-MSF wavelets. We examine the relationship between different classes of wavelets admitting linear phases. In particular we present an example of a non-MSF wavelet which is not an MRA wavelet but admits linear phase 1/2 s. (C) 2002 American Institute of Physics.

    Journal Title

    Journal of Mathematical Physics

    Volume

    43

    Issue/Number

    5

    Publication Date

    1-1-2002

    Document Type

    Article

    Language

    English

    First Page

    2690

    Last Page

    2706

    WOS Identifier

    WOS:000175145100036

    ISSN

    0022-2488

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