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.

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

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

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

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

[Contents of the CD are available for download for readers of the paperback edition.]

C.1 CD Folders    467

C.2 Utility Files Description    467

Index          471

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