Computing the Minimum-Phase Filter using the QL-Factorization

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

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    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
    Issue number6
    Pages (from-to)3195-3205
    Publication statusPublished - 2010

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    Copyright: 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE


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


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