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

534 Pages·2013·19.62 MB·English

by  Steven M. Kay

Fundamentals of Statistical Signal
Processing, Volume III
Practical Algorithm Development
Steven M. Kay
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Library of Congress Control Number: 92029495
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ISBN-13: 978-0-13-280803-3
ISBN-10: 0-13-280803-X
Text printed in the United States on recycled paper at Courier Corporation in
Westford, Massachusetts
Westford, Massachusetts
First printing, March 2013.
To my wife Cindy, who is and will always be my anchor
Contents
Preface
About the Author
I Methodology and General Approaches
1 Introduction
1.1 Motivation and Purpose
1.2 Core Algorithms
1.3 Easy, Hard, and Impossible Problems
1.4 Increasing Your Odds for Success—Enhance Your Intuition
1.5 Application Areas
1.6 Notes to the Reader
1.7 Lessons Learned
References
1A Solutions to Exercises
2 Methodology for Algorithm Design
2.1 Introduction
2.2 General Approach
2.3 Example of Signal Processing Algorithm Design
2.4 Lessons Learned
References
2A Derivation of Doppler Effect
2B Solutions to Exercises
3 Mathematical Modeling of Signals
3.1 Introduction
3.2 The Hierarchy of Signal Models
3.3 Linear vs. Nonlinear Deterministic Signal Models
3.4 Deterministic Signals with Known Parameters (Type 1)
3.5 Deterministic Signals with Unknown Parameters (Type 2)
3.6 Random Signals with Known PDF (Type 3)
3.7 Random Signals with PDF Having Unknown Parameters
3.8 Lessons Learned
References
3A Solutions to Exercises
4 Mathematical Modeling of Noise
4.1 Introduction
4.2 General Noise Models
4.3 White Gaussian Noise
4.4 Colored Gaussian Noise
4.5 General Gaussian Noise
4.6 IID NonGaussian Noise
4.7 Randomly Phased Sinusoids
4.8 Lessons Learned
References
4A Random Process Concepts and Formulas
4B Gaussian Random Processes
4C Geometrical Interpretation of AR PSD
4D Solutions to Exercises
5 Signal Model Selection
5.1 Introduction
5.2 Signal Modeling
5.3 An Example
5.4 Estimation of Parameters
5.5 Model Order Selection
5.6 Lessons Learned
References
5A Solutions to Exercises
6 Noise Model Selection
6.1 Introduction
6.2 Noise Modeling
6.3 An Example
6.4 Estimation of Noise Characteristics
6.5 Model Order Selection
6.6 Lessons Learned
References
6A Confidence Intervals
6B Solutions to Exercises
7 Performance Evaluation, Testing, and Documentation
7.1 Introduction
7.2 Why Use a Computer Simulation Evaluation?
7.3 Statistically Meaningful Performance Metrics
7.4 Performance Bounds
7.5 Exact versus Asymptotic Performance
7.6 Sensitivity
7.7 Valid Performance Comparisons
7.8 Performance/Complexity Tradeoffs
7.9 Algorithm Software Development
7.10 Algorithm Documentation
7.11 Lessons Learned
References
7A A Checklist of Information to Be Included in Algorithm Description
Document
7B Example of Algorithm Description Document
7C Solutions to Exercises
8 Optimal Approaches Using the Big Theorems
8.1 Introduction
8.2 The Big Theorems
8.3 Optimal Algorithms for the Linear Model
8.4 Using the Theorems to Derive a New Result
8.5 Practically Optimal Approaches
8.6 Lessons Learned
References
8A Some Insights into Parameter Estimation
8B Solutions to Exercises
II Specific Algorithms
9 Algorithms for Estimation
9.1 Introduction
9.2 Extracting Signal Information
9.3 Enhancing Signals Corrupted by Noise/Interference
References
9A Solutions to Exercises
10 Algorithms for Detection
10.1 Introduction
10.2 Signal with Known Form (Known Signal)
10.3 Signal with Unknown Form (Random Signals)
10.4 Signal with Unknown Parameters
References
10A Solutions to Exercises
11 Spectral Estimation
11.1 Introduction
11.2 Nonparametric (Fourier) Methods
11.3 Parametric (Model-Based) Spectral Analysis
11.4 Time-Varying Power Spectral Densities
References
11A Fourier Spectral Analysis and Filtering
11B The Issue of Zero Padding and Resolution