About the Author xiii
Preface xv
Acknowledgments xxv
Glossary xxvi
About the Companion Website xxx
1 Introduction 1
1.1 Background 1
1.2 Spectral Decomposition 4
1.3 Data Decomposition 6
1.4 Model-based Decomposition 13
1.5 Notation and Terminology 24
1.6 Summary 25
MATLAB® Notes 26
References 26
Problems 27
2 Random Signals and Systems 31
2.1 Introduction 31
2.2 Discrete Random Signals 34
2.3 Spectral Representation of Random Signals 38
2.4 Discrete Systems with Random Inputs 41
2.5 Classical Spectral Estimation 44
2.6 Case Study: Sinusoids in Noise 52
2.7 Summary 54
MATLAB® Notes 55
References 55
Problems 56
3 Signal Models 61
3.1 Data-Based Models 61
3.2 Parametric-Based Models 65
3.3 State-space Models 85
3.4 Summary 103
MATLAB® Notes 103
References 104
Problems 105
4 Signal Estimation 111
4.1 Classical Estimation 111
4.2 Minimum Variance (MV) Estimation 116
4.3 Maximum A-Posteriori (MAP) Estimation 119
4.4 Maximum Likelihood (ML) Estimation 121
4.5 Least-squares (LS) Estimation 124
4.6 Optimal Signal Estimation 133
4.7 Projection Theory 137
4.8 Summary 142
MATLAB® Notes 142
References 143
Problems 144
5 Signal Decomposition 149
5.1 Introduction 149
5.2 Data-Based Decompositions 149
5.3 Spectral-Based Decompositions 168
5.4 Model-Based Decomposition 179
5.5 Case Study: Harmonics in Noise 198
5.6 Summary 201
MATLAB® Notes 201
References 202
Problems 206
6 Model-based Decomposition: Time Domain 211
6.1 Background: State-space Systems 211
6.2 Realization Problem 220
6.3 Realization Decomposition 228
6.4 Subspace Decomposition: Orthogonal Projections 233
6.5 Subspace Decomposition: Oblique Projections 244
6.6 System Order Estimation and Validation 253
6.7 Case Study: Multichannel Mechanical Systems 259
6.8 Summary 267
MATLAB® Notes 268
References 268
Problems 270
7 Model-Based Decomposition: Frequency Domain 279
7.1 Introduction 279
7.2 Frequency Response Functions (FRF) 282
7.3 Least-squares Complex Frequency (LSCF) Method 295
7.4 PolyReference Least-Squares Complex Frequency (pLSCF) Method 301
7.5 Maximum Likelihood PolyReference Frequency Domain Estimation (ML-pLSCF) 307
7.6 Case Study: 15-DOF Structure 312
7.7 Summary 320
MATLAB® Notes 322
References 322
Problems 324
8 Performance Analysis 329
8.1 Statistical Performance Methods 329
8.2 Physical Performance Metrics 344
8.3 Case Study: Resonant Modal MCK System 352
8.4 Summary 355
MATLAB® Notes 355
References 355
9 Applications 359
9.1 Modal Decomposition: Sounding Rocket Flight 359
9.2 Vibrational Response of a Cylindrical Structure: Identification and Modal Tracking 370
9.3 Resonant Ultrasound Spectroscopy 377
9.4 Model-Based Subsystem Decomposition of an 8-Story (8-Mass) Structure 390
9.5 Data-Based Decomposition: Time-Reversal Processing 403
References 413
A Probability and Statistics Overview 417
A.1 Probability Theory 417
A.2 Gaussian Random Vectors 422
A.3 Uncorrelated Transformation: Gaussian Random Vectors 423
A.4 Toeplitz Correlation Matrices 424
A.5 Important Processes 424
References 426
B Projection Theory 427
B.1 Projections: Deterministic Spaces 427
B.2 Projections: Random Spaces 428
B.3 Projection: Operators 429
B.3.1 Orthogonal (Perpendicular) Projections 429
B.3.2 Oblique (Parallel) Projections 430
References 432
C Matrix Decompositions 433
C.1 Singular Value Decomposition 433
C.2 QR Decomposition 435
C.3 LQ Decomposition 435
References 436
Index 437
