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Fundamentals of Statistical Signal Processing, Volume III: Practical Algorithm Development

Book Description

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.

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

  1. Title Page
  2. Copyright Page
  3. Dedication Page
  4. Contents
  5. Preface
  6. About the Author
  7. Part I. Methodology and General Approaches
    1. Chapter 1. Introduction
      1. 1.1. Motivation and Purpose
      2. 1.2. Core Algorithms
      3. 1.3. Easy, Hard, and Impossible Problems
      4. 1.4. Increasing Your Odds for Success—Enhance Your Intuition
      5. 1.5. Application Areas
      6. 1.6. Notes to the Reader
      7. 1.7. Lessons Learned
      8. References
      9. Appendix 1A. Solutions to Exercises
    2. Chapter 2. Methodology for Algorithm Design
      1. 2.1. Introduction
      2. 2.2. General Approach
      3. 2.3. Example of Signal Processing Algorithm Design
      4. 2.4. Lessons Learned
      5. References
      6. Appendix 2A. Derivation of Doppler Effect
      7. Appendix 2B. Solutions to Exercises
    3. Chapter 3. Mathematical Modeling of Signals
      1. 3.1. Introduction
      2. 3.2. The Hierarchy of Signal Models
      3. 3.3. Linear vs. Nonlinear Deterministic Signal Models
      4. 3.4. Deterministic Signals with Known Parameters (Type 1)
      5. 3.5. Deterministic Signals with Unknown Parameters (Type 2)
      6. 3.6. Random Signals with Known PDF (Type 3)
      7. 3.7. Random Signals with PDF Having Unknown Parameters (Type 4)
      8. 3.8. Lessons Learned
      9. References
      10. Appendix 3A. Solutions to Exercises
    4. Chapter 4. Mathematical Modeling of Noise
      1. 4.1. Introduction
      2. 4.2. General Noise Models
      3. 4.3. White Gaussian Noise
      4. 4.4. Colored Gaussian Noise
      5. 4.5. General Gaussian Noise
      6. 4.6. IID NonGaussian Noise
      7. 4.7. Randomly Phased Sinusoids
      8. 4.8. Lessons Learned
      9. References
      10. Appendix 4A. Random Process Concepts and Formulas
      11. Appendix 4B. Gaussian Random Processes
      12. Appendix 4C. Geometrical Interpretation of AR PSD
      13. Appendix 4D. Solutions to Exercises
    5. Chapter 5. Signal Model Selection
      1. 5.1. Introduction
      2. 5.2. Signal Modeling
      3. 5.3. An Example
      4. 5.4. Estimation of Parameters
      5. 5.5. Model Order Selection
      6. 5.6. Lessons Learned
      7. References
      8. Appendix 5A. Solutions to Exercises
    6. Chapter 6. Noise Model Selection
      1. 6.1. Introduction
      2. 6.2. Noise Modeling
      3. 6.3. An Example
      4. 6.4. Estimation of Noise Characteristics
      5. 6.5. Model Order Selection
      6. 6.6. Lessons Learned
      7. References
      8. Appendix 6A. Confidence Intervals
      9. Appendix 6B. Solutions to Exercises
    7. Chapter 7. Performance Evaluation, Testing, and Documentation
      1. 7.1. Introduction
      2. 7.2. Why Use a Computer Simulation Evaluation?
      3. 7.3. Statistically Meaningful Performance Metrics
      4. 7.4. Performance Bounds
      5. 7.5. Exact versus Asymptotic Performance
      6. 7.6. Sensitivity
      7. 7.7. Valid Performance Comparisons
      8. 7.8. Performance/Complexity Tradeoffs
      9. 7.9. Algorithm Software Development
      10. 7.10. Algorithm Documentation
      11. 7.11. Lessons Learned
      12. References
      13. Appendix 7A. A Checklist of Information to Be Included in Algorithm Description Document
      14. Appendix 7B. Example of Algorithm Description Document
      15. Appendix 7C. Solutions to Exercises
    8. Chapter 8. Optimal Approaches Using the Big Theorems
      1. 8.1. Introduction
      2. 8.2. The Big Theorems
      3. 8.3. Optimal Algorithms for the Linear Model
      4. 8.4. Using the Theorems to Derive a New Result
      5. 8.5. Practically Optimal Approaches
      6. 8.6. Lessons Learned
      7. References
      8. Appendix 8A. Some Insights into Parameter Estimation
      9. Appendix 8B. Solutions to Exercises
  8. Part II. Specific Algorithms
    1. Chapter 9. Algorithms for Estimation
      1. 9.1. Introduction
      2. 9.2. Extracting Signal Information
      3. 9.3. Enhancing Signals Corrupted by Noise/Interference
      4. References
      5. Appendix 9A. Solutions to Exercises
    2. Chapter 10. Algorithms for Detection
      1. 10.1. Introduction
      2. 10.2. Signal with Known Form (Known Signal)
      3. 10.3. Signal with Unknown Form (Random Signals)
      4. 10.4. Signal with Unknown Parameters (Partially Known Signal)
      5. References
      6. Appendix 10A. Solutions to Exercises
    3. Chapter 11. Spectral Estimation
      1. 11.1. Introduction
      2. 11.2. Nonparametric (Fourier) Methods
      3. 11.3. Parametric (Model-Based) Spectral Analysis
      4. 11.4. Time-Varying Power Spectral Densities
      5. References
      6. Appendix 11A. Fourier Spectral Analysis and Filtering
      7. Appendix 11B. The Issue of Zero Padding and Resolution
      8. Appendix 11C. Solutions to Exercises
  9. Part III. Real-World Extensions
    1. Chapter 12. Complex Data Extensions
      1. 12.1. Introduction
      2. 12.2. Complex Signals
      3. 12.3. Complex Noise
      4. 12.4. Complex Least Squares and the Linear Model
      5. 12.5. Algorithm Extensions for Complex Data
      6. 12.6. Other Extensions
      7. 12.7. Lessons Learned
      8. References
      9. Appendix 12A. Solutions to Exercises
  10. Part IV. Real-World Applications
    1. Chapter 13. Case Studies - Estimation Problem
      1. 13.1. Introduction
      2. 13.2. Estimation Problem - Radar Doppler Center Frequency
      3. 13.3. Lessons Learned
      4. References
      5. Appendix 13A. 3 dB Bandwidth of AR PSD
      6. Appendix 13B. Solutions to Exercises
    2. Chapter 14. Case Studies - Detection Problem
      1. 14.1. Introduction
      2. 14.2. Detection Problem - Magnetic Signal Detection
      3. 14.3. Lessons Learned
      4. References
      5. Appendix 14A. Solutions to Exercises
    3. Chapter 15. Case Studies - Spectral Estimation Problem
      1. 15.1. Introduction
      2. 15.2. Extracting the Muscle Noise
      3. 15.3. Spectral Analysis of Muscle Noise
      4. 15.4. Enhancing the ECG Waveform
      5. 15.5. Lessons Learned
      6. References
      7. Appendix 15A. Solutions to Exercises
  11. Appendix A. Glossary of Symbols and Abbreviations
    1. A.1. Symbols
    2. A.2. Abbreviations
  12. Appendix B. Brief Introduction to MATLAB
    1. B.1. Overview of MATLAB
    2. B.2. Plotting in MATLAB
  13. Appendix C. Description of CD Contents
    1. C.1. CD Folders
    2. C.2. Utility Files Description
  14. Index
  15. CD-ROM Warranty
  16. Where Are the Companion Content Files?