Computing the Minimum-Phase Filter using the QL-Factorization

Morten Hansen, Lars P.B. Christensen, Ole Winther

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    Abstract

    We investigate the QL-factorization of a time-invariant convolutive filtering matrix and show that this factorization not only provides the finite length equivalent to the minimum-phase filter, but also gives the associated all-pass filter. The convergence properties are analyzed and we derive the exact convergence rate and an upper bound for a simple Single-Input Single-Output system with filter length = 2 Finally, this upper bound is used to derive an approximation of the convergence rate for systems of arbitrary length. Implementation-wise, the method has the advantage of being numerically stable and straight forward to extend to the Multiple-Input Multiple-Output case. Furthermore, due to the existence of fast QL-factorization methods, it is possible to compute the filters efficiently.
    Original languageEnglish
    JournalI E E E Transactions on Signal Processing
    Volume58
    Issue number6
    Pages (from-to)3195-3205
    ISSN1053-587X
    DOIs
    Publication statusPublished - 2010

    Bibliographical note

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    Keywords

    • Minimum-phase filtering
    • QL-factorization
    • wireless communications
    • spectral factorization
    • sphere detection

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