Fundamentals of Statistical Signal Processing, Volume III: Practical Algorithm Development

Overview

The Complete, Modern Guide to Developing Well-Performing Signal Processing Algorithms

In Fundamentals of Statistical Signal Processing, Volume III: Practical Algorithm Development, author Steven M. Kay shows how to convert theories of statistical signal processing estimation and detection into software algorithms that can be implemented on digital computers. This final volume of Kay’s three-volume guide builds on the comprehensive theoretical coverage in the first two volumes. ...

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Fundamentals of Statistical Signal Processing, Volume III: Practical Algorithm Development

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Overview

The Complete, Modern Guide to Developing Well-Performing Signal Processing Algorithms

In Fundamentals of Statistical Signal Processing, Volume III: Practical Algorithm Development, author Steven M. Kay shows how to convert theories of statistical signal processing estimation and detection into software algorithms that can be implemented on digital computers. This final volume of Kay’s three-volume guide builds on the comprehensive theoretical coverage in the first two volumes. Here, Kay helps readers develop strong intuition and expertise in designing well-performing algorithms that solve real-world problems.

Kay begins by reviewing methodologies for developing signal processing algorithms, including mathematical modeling, computer simulation, and performance evaluation. He links concepts to practice by presenting useful analytical results and implementations for design, evaluation, and testing. Next, he highlights specific algorithms that have “stood the test of time,” offers realistic examples from several key application areas, and introduces useful extensions. Finally, he guides readers through translating mathematical algorithms into MATLAB® code and verifying solutions.

Topics covered include

  • Step by step approach to the design of algorithms
  • Comparing and choosing signal and noise models
  • Performance evaluation, metrics, tradeoffs, testing, and documentation
  • Optimal approaches using the “big theorems”
  • Algorithms for estimation, detection, and spectral estimation
  • Complete case studies: Radar Doppler center frequency estimation, magnetic signal detection, and heart rate monitoring

Exercises are presented throughout, with full solutions, and executable MATLAB code that implements all the algorithms, is provided on the accompanying CD.

This new volume is invaluable to engineers, scientists, and advanced students in every discipline that relies on signal processing; researchers will especially appreciate its timely overview of the state of the practical art. Volume III complements Dr. Kay’s Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (Prentice Hall, 1993; ISBN-13: 978-0-13-345711-7), and Volume II: Detection Theory (Prentice Hall, 1998; ISBN-13: 978-0-13-504135-2).

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Product Details

  • ISBN-13: 9780132808033
  • Publisher: Prentice Hall
  • Publication date: 4/9/2013
  • Edition number: 1
  • Pages: 475
  • Product dimensions: 9.20 (w) x 7.00 (h) x 1.30 (d)

Meet the Author

Steven M. Kay is one of the world’s leading experts in statistical signal processing. Currently Professor of Electrical Engineering at the University of Rhode Island, Kingston, he has consulted for numerous industrial concerns, the Air Force, Army, and Navy, and has taught short courses to scientists and engineers at NASA and the CIA. Dr. Kay is a Fellow of the IEEE, and a member of Tau Beta Pi, and Sigma Xi and Phi Kappa Phi. He has received the Education Award for “outstanding contributions in education and in writing scholarly book and texts…” from the IEEE Signal Processing society and has been listed as among the 250 most cited researchers in the world in engineering.

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Table of Contents

Preface xiii

About the Author xvii

Part I: Methodology and General Approaches 1

Chapter 1: Introduction 3

1.1 Motivation and Purpose 3

1.2 Core Algorithms 4

1.3 Easy, Hard, and Impossible Problems 5

1.4 Increasing Your Odds for Success–Enhance Your Intuition 11

1.5 Application Areas 13

1.6 Notes to the Reader 14

1.7 Lessons Learned 15

References 16

1A Solutions to Exercises 19

Chapter 2: Methodology for Algorithm Design 23

2.1 Introduction 23

2.2 General Approach 23

2.3 Example of Signal Processing Algorithm Design 31

2.4 Lessons Learned 47

References 48

2A Derivation of Doppler Effect 49

2B Solutions to Exercises 53

Chapter 3: Mathematical Modeling of Signals 55

3.1 Introduction 55

3.2 The Hierarchy of Signal Models 57

3.3 Linear vs. Nonlinear Deterministic Signal Models 61

3.4 Deterministic Signals with Known Parameters (Type 1) 62

3.5 Deterministic Signals with Unknown Parameters (Type 2) 68

3.6 Random Signals with Known PDF (Type 3) 77

3.7 Random Signals with PDF Having Unknown Parameters 83

3.8 Lessons Learned 83

References 83

3A Solutions to Exercises 85

Chapter 4: Mathematical Modeling of Noise 89

4.1 Introduction 89

4.2 General Noise Models 90

4.3 White Gaussian Noise 93

4.4 Colored Gaussian Noise 94

4.5 General Gaussian Noise 102

4.6 IID NonGaussian Noise 108

4.7 Randomly Phased Sinusoids 113

4.8 Lessons Learned 114

References 115

4A Random Process Concepts and Formulas 117

4B Gaussian Random Processes 119

4C Geometrical Interpretation of AR 121

4D Solutions to Exercises 123

Chapter 5: Signal Model Selection 129

5.1 Introduction 129

5.2 Signal Modeling 130

5.3 An Example 131

5.4 Estimation of Parameters 136

5.5 Model Order Selection 138

5.6 Lessons Learned 142

References 143

5A Solutions to Exercises 145

Chapter 6: Noise Model Selection 149

6.1 Introduction 149

6.2 Noise Modeling 150

6.3 An Example 152

6.4 Estimation of Noise Characteristics 161

6.5 Model Order Selection 176

6.6 Lessons Learned 177

References 178

6A Confidence Intervals 179

6B Solutions to Exercises 183

Chapter 7: Performance Evaluation, Testing, and Documentation 189

7.1 Introduction 189

7.2 Why Use a Computer Simulation Evaluation? 189

7.3 Statistically Meaningful Performance Metrics 190

7.4 Performance Bounds 202

7.5 Exact versus Asymptotic Performance 204

7.6 Sensitivity 206

7.7 Valid Performance Comparisons 207

7.8 Performance/Complexity Tradeoffs 209

7.9 Algorithm Software Development 210

7.10 Algorithm Documentation 214

7.11 Lessons Learned 215

References 216

7A A Checklist of Information to Be Included in Algorithm Description Document 217

7B Example of Algorithm Description Document 219

7C Solutions to Exercises 231

Chapter 8: Optimal Approaches Using the Big Theorems 235

8.1 Introduction 235

8.2 The Big Theorems 237

8.3 Optimal Algorithms for the Linear Model 251

8.4 Using the Theorems to Derive a New Result 255

8.5 Practically Optimal Approaches 257

8.6 Lessons Learned 261

References 262

8A Some Insights into Parameter Estimation 263

8B Solutions to Exercises 267

Part II: Specific Algorithms 271

Chapter 9: Algorithms for Estimation 273

9.1 Introduction 273

9.2 Extracting Signal Information 274

9.3 Enhancing Signals Corrupted by Noise/Interference 299

References 308

9A Solutions to Exercises 311

Chapter 10: Algorithms for Detection 313

10.1 Introduction 313

10.2 Signal with Known Form (Known Signal) 315

10.3 Signal with Unknown Form (Random Signals) 322

10.4 Signal with Unknown Parameters 326

References 334

10A Solutions to Exercises 337

Chapter 11: Spectral Estimation 339

11.1 Introduction 339

11.2 Nonparametric (Fourier) Methods 340

11.3 Parametric (Model-Based) Spectral Analysis 348

11.4 Time-Varying Power Spectral Densities 356

References 357

11A Fourier Spectral Analysis and Filtering 359

11B The Issue of Zero Padding and Resolution 361

11C Solutions to Exercises 363

Part III: Real-World Extensions 365

Chapter 12: Complex Data Extensions 367

12.1 Introduction 367

12.2 Complex Signals 371

12.3 Complex Noise 372

12.4 Complex Least Squares and the Linear Model 378

12.5 Algorithm Extensions for Complex Data 379

12.6 Other Extensions 395

12.7 Lessons Learned 396

References 396

12A Solutions to Exercises 399

Part IV: Real-World Applications 403

Chapter 13: Case Studies - Estimation Problem 405

13.1 Introduction 405

13.2 Estimation Problem - Radar Doppler Center Frequency 406

13.3 Lessons Learned 416

References 417

13A 3 dB Bandwidth of AR PSD 419

13B Solutions to Exercises 421

Chapter 14: Case Studies - Detection Problem 423

14.1 Introduction 423

14.2 Detection Problem–Magnetic Signal Detection 423

14.3 Lessons Learned 439

References 439

14A Solutions to Exercises 441

Chapter 15: Case Studies - Spectral Estimation Problem 443

15.1 Introduction 443

15.2 Extracting the Muscle Noise 446

15.3 Spectral Analysis of Muscle Noise 449

15.4 Enhancing the ECG Waveform 451

15.5 Lessons Learned 453

References 453

15A Solutions to Exercises 455

Appendix A: Glossary of Symbols and Abbreviations 457

A.1 Symbols 457

A.2 Abbreviations 459

Appendix B: Brief Introduction to MATLAB 461

B.1 Overview of MATLAB 461

B.2 Plotting in MATLAB 464

Appendix C: Description of CD Contents 467

C.1 CD Folders 467

C.2 Utility Files Description 467

Index 471

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