Fundamentals of Statistical Signal Processing, Volume 3

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 available for download.   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).

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 [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