Fundamentals of Statistical Signal Processing, Volume 3

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). 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. 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 18