Cover -- Title Page -- Copyright -- Contents -- About the Author -- Preface -- Acknowledgments -- Glossary -- About the Companion Website -- Chapter 1 Introduction -- 1.1 Background -- 1.2 Spectral Decomposition -- 1.3 Data Decomposition -- 1.4 Model-based Decomposition -- 1.5 Notation and Terminology -- 1.6 Summary -- MATLAB® Notes -- References -- Problems -- Chapter 2 Random Signals and Systems -- 2.1 Introduction -- 2.2 Discrete Random Signals -- 2.3 Spectral Representation of Random Signals -- 2.4 Discrete Systems with Random Inputs -- 2.5 Classical Spectral Estimation -- 2.5.1 Correlation Method (Blackman-Tukey) -- 2.5.2 Average Periodogram Method (Welch) -- 2.5.3 Minimum Variance Distortionless Response (MVDR) -- 2.5.4 Coherence Function -- 2.6 Case Study: Sinusoids in Noise -- 2.7 Summary -- MATLAB® Notes -- References -- Problems -- Chapter 3 Signal Models -- 3.1 Data-Based Models -- 3.1.1 Data-Based Response Matrices -- 3.1.2 Data-Based Toeplitz Matrices -- 3.1.3 Data-Based Hankel Matrices -- 3.2 Parametric-Based Models -- 3.2.1 ARMAX (AR, ARX, MA, ARMA) Models -- 3.2.2 Lattice Models -- 3.2.3 Transfer Function/Frequency Response Function Models -- 3.2.4 Harmonic Models -- 3.3 State-space Models -- 3.3.1 Continuous-time State-space Models -- 3.3.2 Sampled-data State-space Models -- 3.3.3 Discrete-time State-space Models -- 3.3.4 Gauss-Markov State-space Models -- 3.3.5 Innovations Model -- 3.3.6 State-space Equivalence Models -- 3.4 Summary -- MATLAB® Notes -- References -- Problems -- Chapter 4 Signal Estimation -- 4.1 Classical Estimation -- 4.1.1 Estimator Properties -- 4.1.2 Estimator Performance -- 4.2 Minimum Variance (MV) Estimation -- 4.3 Maximum A-Posteriori (MAP) Estimation -- 4.4 Maximum Likelihood (ML) Estimation -- 4.5 Least-squares (LS) Estimation -- 4.5.1 Batch Least Squares -- 4.5.2 Recursive Least-squares.

4.6 Optimal Signal Estimation -- 4.7 Projection Theory -- 4.7.1 Orthogonal Projections: A Geometric Decomposition Perspective -- 4.7.2 Orthogonal Projections: Singular Value Decomposition -- 4.8 Summary -- MATLAB® Notes -- References -- Problems -- Chapter 5 Signal Decomposition -- 5.1 Introduction -- 5.2 Data-Based Decompositions -- 5.2.1 Data Decomposition: Principal Component Analysis (PCA) -- 5.2.2 Data Decomposition: Independent Component Analysis (ICA) -- 5.2.2.1 Higher Order Statistics -- 5.2.2.2 Information Theory: Negentropy -- 5.2.2.3 Information Theory: Mutual Information -- 5.2.2.4 Estimation Theory: Maximum Likelihood -- 5.2.3 Data Decomposition: Singular Spectral Analysis (SSA) -- 5.3 Spectral-Based Decompositions -- 5.3.1 Spectral Decomposition: Multitaper Method (MTM) -- 5.3.2 Spectral Decomposition: Subspace Method -- 5.3.3 Spectral Decomposition: Pisarenko Harmonic Decomposition (PHD) Method -- 5.3.4 Spectral Decomposition: Multiple Signal Classification (MUSIC) Method -- 5.4 Model-Based Decomposition -- 5.4.1 Model-Based Decomposition: Damped Exponential Method -- 5.4.2 Model-Based Decomposition: Lattice Method -- 5.4.3 Model-Based Decomposition: State-Space Method -- 5.5 Case Study: Harmonics in Noise -- 5.6 Summary -- MATLAB® Notes -- References -- Problems -- Chapter 6 Model-based Decomposition: Time Domain -- 6.1 Background: State-space Systems -- 6.1.1 Discrete Systems Theory -- 6.1.2 Stable Linear Systems -- 6.1.3 Equivalent Linear Systems -- 6.1.4 Modal Systems -- 6.2 Realization Problem -- 6.2.1 Realization Theory -- 6.2.2 Balanced Realizations -- 6.2.3 Systems Theory Summary -- 6.3 Realization Decomposition -- 6.3.1 Ho-Kalman Realization -- 6.3.2 SVD Realization -- 6.4 Subspace Decomposition: Orthogonal Projections -- 6.4.1 Subspace Realization: Orthogonal Projections.

6.4.2 Multivariable Output Error State-space (MOESP) Algorithm -- 6.5 Subspace Decomposition: Oblique Projections -- 6.5.1 Subspace Realization: Oblique Projections -- 6.5.2 Numerical Algorithms for Subspace State-space System Identification (N4SID) -- 6.6 System Order Estimation and Validation -- 6.6.1 Order Estimation: SVD Approach -- 6.6.2 Model Validation -- 6.7 Case Study: Multichannel Mechanical Systems -- 6.7.1 Mechanical Systems -- 6.7.2 Case Study: 3-mass Mechanical System -- 6.8 Summary -- MATLAB® Notes -- References -- Problems -- Chapter 7 Model-Based Decomposition: Frequency Domain -- 7.1 Introduction -- 7.1.1 Background -- 7.2 Frequency Response Functions (FRF) -- 7.2.1 FRF Estimation: Impulse Response Method -- 7.2.2 FRF Spectral Estimation: Polynomial Models -- 7.2.3 FRF-Spectral Estimation: Power Spectra -- 7.2.4 FRF-Spectral Estimation: Frequency Domain Decomposition (FDD) Method -- 7.2.4.1 Power Spectral Density Decomposition -- 7.2.4.2 Complex Mode Indicator Function (CMIF) -- 7.2.5 Stabilization Diagram (SDIAG) -- 7.3 Least-squares Complex Frequency (LSCF) Method -- 7.4 PolyReference Least-Squares Complex Frequency (pLSCF) Method -- 7.5 Maximum Likelihood PolyReference Frequency Domain Estimation (ML-pLSCF) -- 7.6 Case Study: 15-DOF Structure -- 7.7 Summary -- MATLAB® Notes -- References -- Problems -- Chapter 8 Performance Analysis -- 8.1 Statistical Performance Methods -- 8.1.1 Zero-Mean Test -- 8.1.2 Whiteness Test -- 8.1.3 Weighted Sum-Squared Residual Test -- 8.1.4 Standard Error Test -- 8.1.5 Correlation Coefficient Function Test -- 8.1.6 Coherence Function Test -- 8.1.7 Ensemble Tests -- 8.1.8 Statistical Order Estimation -- 8.1.9 Signal (Model) Validation -- 8.1.10 MAD Signal Validation -- 8.2 Physical Performance Metrics -- 8.2.1 Spectral Peaks: Picking/Histogram -- 8.2.2 Modal Assurance Criterion (MAC).

8.2.3 Hankel/SVD Criteria -- 8.2.4 Modal Observability Correlation (MOC) Criterion -- 8.2.5 Modal Singular Value (MSV) Criterion -- 8.2.6 Stabilization Diagram (SDIAG) -- 8.2.7 Modal Frequency Tracker -- 8.3 Case Study: Resonant Modal MCK System -- 8.4 Summary -- MATLAB® Notes -- References -- Chapter 9 Applications -- 9.1 Modal Decomposition: Sounding Rocket Flight -- 9.1.1 Experimental Test Unit Design and Analysis -- 9.1.2 Sounding Rocket Flight Testing -- 9.1.3 Summary -- 9.2 Vibrational Response of a Cylindrical Structure: Identification and Modal Tracking -- 9.2.1 Summary -- 9.3 Resonant Ultrasound Spectroscopy -- 9.3.1 RUS Methodology -- 9.3.2 Modal Analysis: FRF and Frequency Histogram -- 9.3.3 Model-Based Decomposition Approach -- 9.3.4 Application: Parallel Piped Structure -- 9.3.4.1 Synthesized Data: RPP Structure -- 9.3.5 Experimental Data: RPP Structure -- 9.3.6 Model-Based Decomposition Processor -- 9.3.7 Elastic Coefficient Estimation -- 9.3.8 Summary -- 9.4 Model-Based Subsystem Decomposition of an 8-Story (8-Mass) Structure -- 9.4.1 Subspace Structural Identification -- 9.4.2 Shaping Filters -- 9.4.3 Subsystem Modal Extraction -- 9.4.4 Summary -- 9.5 Data-Based Decomposition: Time-Reversal Processing -- 9.5.1 Iterative Time-Reversal Decomposition -- 9.5.2 Eigen-decomposition Time-reversal Extraction -- 9.5.3 Summary -- References -- A Probability and Statistics Overview -- A.1 Probability Theory -- A.2 Gaussian Random Vectors -- A.3 Uncorrelated Transformation: Gaussian Random Vectors -- A.4 Toeplitz Correlation Matrices -- A.5 Important Processes -- References -- B Projection Theory -- B.1 Projections: Deterministic Spaces -- B.2 Projections: Random Spaces -- B.3 Projection: Operators -- B.3.1 Orthogonal (Perpendicular) Projections -- B.3.2 Oblique (Parallel) Projections -- References -- C Matrix Decompositions.

C.1 Singular Value Decomposition -- C.2 QR Decomposition -- C.3 LQ Decomposition -- References -- Index -- EULA.