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.
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- Minimum-phase filtering
- wireless communications
- spectral factorization
- sphere detection
Hansen, M., Christensen, L. P. B., & Winther, O. (2010). Computing the Minimum-Phase Filter using the QL-Factorization. I E E E Transactions on Signal Processing, 58(6), 3195-3205. https://doi.org/10.1109/TSP.2010.2045795