Spectrum Estimation and System Identification

1 Introduction.- 1.1 Introduction.- 1.2 Organization of the Book.- 1.3 Notations and Preliminaries.- 2 Power Spectra and Positive Functions.- 2.1 Stationary Processes and Power Spectra.- 2.1.1 Linear Prediction.- 2.2 Positive Functions.- 2.2.1 Bounded Functions.- 2.2.2 Schur Algorithm and Line Extraction.- Problems.- 3 Admissible Spectral Extensions.- 3.1 Introduction.- 3.2 Geometrical Solution.- 3.3 Parametrization of Admissible Extensions.- 3.3.1 Levinson Polynomials and Reflection Coefficients.- 3.3.2 Reflection Coefficients and Characteristic Impedances.- 3.4 Two-Step Predictor.- Appendix 3.A Maximization of the k-Step Minimum Mean-Square Prediction Error.- Appendix 3.B Uniqueness of ?(z).- Appendix 3.C Negative Discriminant.- Appendix 3.D Existence of the Second Bounded-Real Solution.- Problems.- 4 ARMA-System Identification and Rational Approximation.- 4.1 Introduction.- 4.1.1 Exact Autocorrelations Case.- 4.1.2 Known Data Case.- 4.2 ARMA-System Identification - A New Approach.- 4.2.1 ARMA-System Characterization.- 4.2.2 ARMA-Parameter Estimation.- 4.2.3 Model Order Selection.- 4.2.4 Simulation Results.- 4.3 Rational Approximation of Nonrational Systems.- 4.3.1 Pade-like Approximation.- 4.3.2 Numerical Results.- Appendix 4.A A Necessary Condition for Pade-like Approximation.- Appendix 4.B Diagonal Pade Approximations of e-p.- Problems.- 5 Multichannel System Identification.- 5.1 Introduction.- 5.2 Multichannel Admissible Spectral Extensions.- 5.2.1 Multichannel Schur Algorithm and a Weak Form of Richards' Theorem.- 5.2.2 Left-Inverse Form.- 5.2.3 Right-Inverse Form.- 5.2.4 Multichannel Spectral Extension - Youla's Representation.- 5.3 Multichannel Rational System Identification.- 5.3.1 MARMA System Characterization.- 5.3.2 MARMA Parameter Estimation.- 5.3.3 Model Order Selection.- 5.3.4 Simulation Results.- 5.4 Multichannel Rational Approximation of Nonrational Systems.- 5.4.1 Multichannel Pade-like Approximation.- Appendix 5.A Reflection Coefficient Matrices and Their Left and Right Factors.- Appendix 5.B Renormalization of dn (z).- Problems.- References.