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Signal Processing
An Applied Decomposition Approach

James V. Candy (Author)

9781394207442, Wiley

Hardback, published 2 October 2024

480 pages
22.9 x 15.2 x 2.9 cm, 0.875 kg

Separate signals from noise with this valuable introduction to signal processing by applied decomposition

The decomposition of complex signals into the sub-signals, or individual components, is a crucial tool in signal processing. It allows each component of a signal to be analyzed individually, enables the signal to be isolated from noise, and processed in full. Decomposition processes have not always been widely adopted due to the difficult underlying mathematics and complex applications. This text simplifies these obstacles.

Signal Processing: An Applied Decomposition Approach demystifies these tools from a model-based perspective. This offers a mathematically informed, “step-by-step” analysis of the process by breaking down a composite signal/system into its constituent parts, while introducing both fundamental concepts and advanced applications. This comprehensive approach addresses each of the major decomposition techniques, making it an indispensable addition to any library specializing in signal processing.

Signal Processing readers will find:

  • Signal decomposition techniques developed from the data-based, spectral-based and model-based perspectives incorporate: statistical approaches (PCA, ICA, Singular Spectrum); spectral approaches (MTM, PHD, MUSIC); and model-based approaches (EXP, LATTICE, SSP)
  • In depth discussion of topics includes signal/system estimation and decomposition, time domain and frequency domain techniques, systems theory, modal decompositions, applications and many more
  • Numerous figures, examples, and tables illustrating key concepts and algorithms are developed throughout the text
  • Includes problem sets, case studies, real-world applications as well as MATLAB notes highlighting applicable commands

Signal Processing is ideal for engineering and scientific professionals, as well as graduate students seeking a focused text on signal/system decomposition with performance metrics and real-world applications.

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

Subject Areas: Electronics & communications engineering [TJ]
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