Efficient Schur Parametrization and Modeling of p-Stationary Second-Order Time-Series for LPC Transmission

• Autorzy: Wielgus A. , Zarzycki J.

Identyfikatory

DOI

10.24425/123531

• Języki publikacji: EN

Abstrakty

EN

Following the results presented in [21], we present an efficient approach to the Schur parametrization/modeling of a subclass of second-order time-series which we term p-stationary time-series, yielding a uniform hierarchy of algorithms suitable for efficient implementations and being a good starting point for nonlinear generalizations to higher-order non-Gaussian nearstationary time-series.

Słowa kluczowe

EN

second-order nonstationary time-series; linear Schur parametrization/modeling; complexity reduction

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2018
• Tom: Vol. 64, No. 3
• Strony: 343--350
• Opis fizyczny: Bibliogr. 24 poz., rys.

Twórcy

autor

Wielgus A.

• Signal Processing Systems Department, Faculty of Electronics, Wroclaw University of Science and Technology, Wroclaw

autor

Zarzycki J.

• Signal Processing Systems Department, Faculty of Electronics, Wroclaw University of Science and Technology, Wroclaw, Poland

Bibliografia

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• [8] T.Kailath, Linear Estimations for Stationary and Near-Stationary Processes, in: Modern Signal Processing, T.Kailath (Ed.), Hemisphere Publishing Corp./Springer-Verlag 1985, pp.59-128.
• [9] T.Kailath, A Theorem of I.Schur and Its Impact on Modern Signal Processing, in: I.Schur Methods in Operator Theory and Signal Processing, I.Gohberg (Ed.), Operator Theory: Advances and Applications, vol.18, Birkhäuser Verlag 1986, pp.9-30.
• [10] T.Kailath, Time-Variant and Time-Invariant Lattice-Filters for Nonstationary Processes, in: Outils et modeles mathematiques pour l’automatique, l’analyse de systemes et le traitement du signal, CNRS (ed.), Paris 1982, pp.417-464.
• [11] T.Kailath, S.Y.Kung, M.Morf, Displacement Ranks of Matrices and Linear Equations, J.Math.Anal.Appl., Volume 68, 1979.
• [12] T.Kailath, Linear Estimations for Stationary and Near-Stationary Processes, in: Modern Signal Processing, T.Kailath (Ed.), Hemisphere Publishing Corp./Springer-Verlag 1985, pp.59-128.
• [13] T.Kailath, S.Kung, M.Morf, Displacement ranks of matrices and linear equations, J. Math. Anal. Appl., 68, pp.396-407, 1979.
• [14] D.T.L.Lee, M.Morf, B.Friedlander, Recursive Least-Squares Ladder Estimation Algorithms, IEEE Trans. on Circuits and Systems, vol. CAS-28, 1981, pp.467-481.
• [15] H.Lev-Ari, T.Kailath, Lattice filter parametrization and modelling of nonstationary processes, IEEE Trans. on Inf. Theory, vol. IT-30, 1984, pp.2-16.
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• [17] F.Lwow, Orthogonal parametrization of random impulse signals as a basis of acoustic exposure evaluation in sport shooting, Ph.D.Thesis, Faculty of Electronics, Wroclaw University of Science and Technology, Techn.Rept. I-28/PRE-032/2000.
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• [19] A.Wielgus, Generalized Versus Classical Kolmogorov Isomorphism for Second-Order Stochastic Processes, submitted for publication.
• [20] A.Wielgus, U.Libal, W.Magiera, Nonlinear Complexity Reduction: Sparsity of the Generalized Schur Coefficient Matrices and Frobenius Norm Criterion, IEEE Signal Processing Symposium (SPSympo-2017).
• [21] A.Wielgus, J.Zarzycki, Efficient Schur Parametrization of Near-Stationary Stochastic Processes, Proc. IWSSIP’2017.
• [22] A.Wielgus, J.Zarzycki, Nonlinear Schur Parametrization and Orthogonal Modeling of p-Stationary Higher-Order Stochastic Processes, Techn. Rept. Wroclaw University of Science and Technology, 2017 (submitted for publication).
• [23] A.Wielgus, J.Zarzycki, F.Lwow, Schur Parametrization and Orthogonal Modeling of p-Stationary Second-Order Stochastic Processes, submitted for publication.
• [24] J.Zarzycki, P. Dewilde, The nonlinear nonstationary Schur algorithm, Proc. Workshop on Advanced Algorithms and Their Realizations, Editor M.Verhaegen (Delft Univ. Techn., Chateaux de Bonas, 1991, paper V3.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).