Real orthogonal polynomials in frequency analysis

    Authors

    C. F. Bracciali; X. Li;A. S. Ranga

    Comments

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    Abbreviated Journal Title

    Math. Comput.

    Keywords

    frequency analysis problem; frequency estimation; orthogonal; polynomials; Szego polynomials; para-orthogonal polynomials; quadrature; SZEGO POLYNOMIALS; UNIT-CIRCLE; CONTINUED FRACTIONS; QUADRATURE; ALGORITHM; ZEROS; Mathematics, Applied

    Abstract

    We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than the Levinson algorithm, for the determination of the reflection coefficients of the corresponding real Szego polynomials from the given moments.

    Journal Title

    Mathematics of Computation

    Volume

    74

    Issue/Number

    249

    Publication Date

    1-1-2004

    Document Type

    Article

    Language

    English

    First Page

    341

    Last Page

    362

    WOS Identifier

    WOS:000224383800016

    ISSN

    0025-5718

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