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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 (R) 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 monitoringExercises 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).
Contents
Preface xiii About the Author xviiPart I: Methodology and General Approaches 1Chapter 1: Introduction 31.1 Motivation and Purpose 31.2 Core Algorithms 41.3 Easy, Hard, and Impossible Problems 51.4 Increasing Your Odds for Success-Enhance Your Intuition 111.5 Application Areas 131.6 Notes to the Reader 141.7 Lessons Learned 15References 161A Solutions to Exercises 19Chapter 2: Methodology for Algorithm Design 232.1 Introduction 232.2 General Approach 232.3 Example of Signal Processing Algorithm Design 312.4 Lessons Learned 47References 482A Derivation of Doppler Effect 492B Solutions to Exercises 53Chapter 3: Mathematical Modeling of Signals 553.1 Introduction 553.2 The Hierarchy of Signal Models 573.3 Linear vs. Nonlinear Deterministic Signal Models 613.4 Deterministic Signals with Known Parameters (Type 1) 623.5 Deterministic Signals with Unknown Parameters (Type 2) 683.6 Random Signals with Known PDF (Type 3) 773.7 Random Signals with PDF Having Unknown Parameters 833.8 Lessons Learned 83References 833A Solutions to Exercises 85Chapter 4: Mathematical Modeling of Noise 894.1 Introduction 894.2 General Noise Models 904.3 White Gaussian Noise 934.4 Colored Gaussian Noise 944.5 General Gaussian Noise 1024.6 IID NonGaussian Noise 1084.7 Randomly Phased Sinusoids 1134.8 Lessons Learned 114References 1154A Random Process Concepts and Formulas 1174B Gaussian Random Processes 1194C Geometrical Interpretation of AR 1214D Solutions to Exercises 123Chapter 5: Signal Model Selection 1295.1 Introduction 1295.2 Signal Modeling 1305.3 An Example 1315.4 Estimation of Parameters 1365.5 Model Order Selection 1385.6 Lessons Learned 142References 1435A Solutions to Exercises 145Chapter 6: Noise Model Selection 1496.1 Introduction 1496.2 Noise Modeling 1506.3 An Example 1526.4 Estimation of Noise Characteristics 1616.5 Model Order Selection 1766.6 Lessons Learned 177References 1786A Confidence Intervals 1796B Solutions to Exercises 183Chapter 7: Performance Evaluation, Testing, and Documentation 1897.1 Introduction 1897.2 Why Use a Computer Simulation Evaluation? 1897.3 Statistically Meaningful Performance Metrics 1907.4 Performance Bounds 2027.5 Exact versus Asymptotic Performance 2047.6 Sensitivity 2067.7 Valid Performance Comparisons 2077.8 Performance/Complexity Tradeoffs 2097.9 Algorithm Software Development 2107.10 Algorithm Documentation 2147.11 Lessons Learned 215References 2167A A Checklist of Information to Be Included in Algorithm Description Document 2177B Example of Algorithm Description Document 2197C Solutions to Exercises 231Chapter 8: Optimal Approaches Using the Big Theorems 2358.1 Introduction 2358.2 The Big Theorems 2378.3 Optimal Algorithms for the Linear Model 2518.4 Using the Theorems to Derive a New Result 2558.5 Practically Optimal Approaches 2578.6 Lessons Learned 261References 2628A Some Insights into Parameter Estimation 2638B Solutions to Exercises 267Part II: Specific Algorithms 271Chapter 9: Algorithms for Estimation 2739.1 Introduction 2739.2 Extracting Signal Information 2749.3 Enhancing Signals Corrupted by Noise/Interference 299References 3089A Solutions to Exercises 311Chapter 10: Algorithms for Detection 31310.1 Introduction 31310.2 Signal with Known Form (Known Signal) 31510.3 Signal with Unknown Form (Random Signals) 32210.4 Signal with Unknown Parameters 326References 33410A Solutions to Exercises 337Chapter 11: Spectral Estimation 33911.1 Introduction 33911.2 Nonparametric (Fourier) Methods 34011.3 Parametric (Model-Based) Spectral Analysis 34811.4 Time-Varying Power Spectral Densities 356References 35711A Fourier Spectral Analysis and Filtering 35911B The Issue of Zero Padding and Resolution 36111C Solutions to Exercises 363Part III: Real-World Extensions 365Chapter 12: Complex Data Extensions 36712.1 Introduction 36712.2 Complex Signals 37112.3 Complex Noise 37212.4 Complex Least Squares and the Linear Model 37812.5 Algorithm Extensions for Complex Data 37912.6 Other Extensions 39512.7 Lessons Learned 396References 39612A Solutions to Exercises 399Part IV: Real-World Applications 403Chapter 13: Case Studies - Estimation Problem 40513.1 Introduction 40513.2 Estimation Problem - Radar Doppler Center Frequency 40613.3 Lessons Learned 416References 41713A 3 dB Bandwidth of AR PSD 41913B Solutions to Exercises 421Chapter 14: Case Studies - Detection Problem 42314.1 Introduction 42314.2 Detection Problem-Magnetic Signal Detection 42314.3 Lessons Learned 439References 43914A Solutions to Exercises 441Chapter 15: Case Studies - Spectral Estimation Problem 44315.1 Introduction 44315.2 Extracting the Muscle Noise 44615.3 Spectral Analysis of Muscle Noise 44915.4 Enhancing the ECG Waveform 45115.5 Lessons Learned 453References 45315A Solutions to Exercises 455Appendix A: Glossary of Symbols and Abbreviations 457A.1 Symbols 457A.2 Abbreviations 459Appendix B: Brief Introduction to MATLAB 461B.1 Overview of MATLAB 461B.2 Plotting in MATLAB 464Appendix C: Description of CD Contents 467C.1 CD Folders 467C.2 Utility Files Description 467Index 471
