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 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).

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 C.1 CD Folders 467 C.2 Utility Files Description 467   Index 471