Journal article
Computing the Minimum-Phase Filter using the QL-Factorization
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.
| Language: | English |
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| Publisher: | IEEE |
| Year: | 2010 |
| Pages: | 3195-3205 |
| ISSN: | 19410476 and 1053587x |
| Types: | Journal article |
| DOI: | 10.1109/TSP.2010.2045795 |
| ORCIDs: | Winther, Ole |
Minimum-phase filtering QL-factorization spectral factorization sphere detection wireless communications
Convergence Delay estimation Digital filters Filtering Finite impulse response filter MIMO QL-factorization methods Signal processing Signal processing algorithms Upper bound Wireless communication all-pass filter all-pass filters approximation theory arbitrary length convergence of numerical methods exact convergence rate filtering theory matrix decomposition minimum-phase filter single-input single-output system time-invariant convolutive filtering matrix
