Computing the Minimum-Phase Filter Using the QL-Factorization
TL;DR: This factorization not only provides the finite length equivalent to the minimum-phase filter, but also gives the associated all-pass filter and an upper bound is used to derive an approximation of the convergence rate for systems of arbitrary length.
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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 . 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.
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Citations
Design of a Simple Orthogonal Multiwavelet Filter by Matrix Spectral Factorization
TL;DR: This work considers the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization, and derives the corresponding Orthogonal multi wavelet SA1 using Bauer’s method.
Matrix spectral factorization for SA4 multiwavelet
TL;DR: Bauer’s method for the matrix spectral factorization of an r-channel matrix product filter which is a half-band autocorrelation matrix is investigated, leading to the approximate and exact orthogonal SA4 multiscaling functions.
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Efficient minimum-phase prefilter computation using fast QL-factorization
Morten Hartvig Hansen,Lars P. B. Christensen +1 more
- 19 Apr 2009
TL;DR: This paper presents a novel approach for computing both the minimum-phase filter and the associated all-pass filter in a computationally efficient way using fast QL-factorization.
Approximate Inference for Wireless Communications
Morten Hansen,Lars P. B. Christensen,Ole Winther +2 more
- 01 Mar 2010
TL;DR: It is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum-phase and all-pass filters and enables us to view Sphere Detection (SD) as an adaptive variant of minimum- phase prefiltered reduced-state sequence estimation.
Design of a Simple Orthogonal Multiwavelet Filter by Matrix Spectral Factorization
TL;DR: In this article, the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization is considered, and a lifting scheme for SA1 is given, and the influence of the number of significant digits in the calculations is investigated.
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