Matrix analysis
QR factorization of toeplitz matrices
Numerische Mathematik
Hybrid algorithm for fast Toeplitz orthogonalization
Numerische Mathematik
Discrete-time signal processing
Discrete-time signal processing
Digital signal processing (3rd ed.): principles, algorithms, and applications
Digital signal processing (3rd ed.): principles, algorithms, and applications
Toeplitz And Circulant Matrices: A Review (Foundations and Trends(R) in Communications and Information Theory)
Efficient minimum-phase prefilter computation using fast QL-factorization
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
On prefilter computation for reduced-state equalization
IEEE Transactions on Wireless Communications
MMSE decision-feedback equalizers: finite-length results
IEEE Transactions on Information Theory
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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 L=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.