Fundamentals of Statistical Signal Processing, Volume 3
- 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
- [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
The Complete, Modern Guide to Developing Well-Performing Signal Processing Algorithms Â
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.
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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.
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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 theoremsâ€
- 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 available for download.
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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).
