| |
| |
Preface | |
| |
| |
About the Author | |
| |
| |
| |
Methodology and General Approaches | |
| |
| |
| |
Introduction | |
| |
| |
| |
Motivation and Purpose | |
| |
| |
| |
Core Algorithms | |
| |
| |
| |
Easy, Hard, and Impossible Problems | |
| |
| |
| |
Increasing Your Odds for Success-Enhance Your Intuition | |
| |
| |
| |
Application Areas | |
| |
| |
| |
Notes to the Reader | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Methodology for Algorithm Design | |
| |
| |
| |
Introduction | |
| |
| |
| |
General Approach | |
| |
| |
| |
Example of Signal Processing Algorithm Design | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Derivation of Doppler Effect | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Mathematical Modeling of Signals | |
| |
| |
| |
Introduction | |
| |
| |
| |
The Hierarchy of Signal Models | |
| |
| |
| |
Linear vs. Nonlinear Deterministic Signal Models | |
| |
| |
| |
Deterministic Signals with Known Parameters (Type 1) | |
| |
| |
| |
Deterministic Signals with Unknown Parameters (Type 2) | |
| |
| |
| |
Random Signals with Known PDF (Type 3) | |
| |
| |
| |
Random Signals with PDF Having Unknown Parameters | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Mathematical Modeling of Noise | |
| |
| |
| |
Introduction | |
| |
| |
| |
General Noise Models | |
| |
| |
| |
White Gaussian Noise | |
| |
| |
| |
Colored Gaussian Noise | |
| |
| |
| |
General Gaussian Noise | |
| |
| |
| |
IID NonGaussian Noise | |
| |
| |
| |
Randomly Phased Sinusoids | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Random Process Concepts and Formulas | |
| |
| |
| |
Gaussian Random Processes | |
| |
| |
| |
Geometrical Interpretation of AR PSD | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Signal Model Selection | |
| |
| |
| |
Introduction | |
| |
| |
| |
Signal Modeling | |
| |
| |
| |
An Example | |
| |
| |
| |
Estimation of Parameters | |
| |
| |
| |
Model Order Selection | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Noise Model Selection | |
| |
| |
| |
Introduction | |
| |
| |
| |
Noise Modeling | |
| |
| |
| |
An Example | |
| |
| |
| |
Estimation of Noise Characteristics | |
| |
| |
| |
Model Order Selection | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Confidence Intervals | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Performance Evaluation, Testing, and Documentation | |
| |
| |
| |
Introduction | |
| |
| |
| |
Why Use a Computer Simulation Evaluation? | |
| |
| |
| |
Statistically Meaningful Performance Metrics | |
| |
| |
| |
Performance Bounds | |
| |
| |
| |
Exact versus Asymptotic Performance | |
| |
| |
| |
Sensitivity | |
| |
| |
| |
Valid Performance Comparisons | |
| |
| |
| |
Performance/Complexity Tradeoffs | |
| |
| |
| |
Algorithm Software Development | |
| |
| |
| |
Algorithm Documentation | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
A Checklist of Information to Be Included in Algorithm Description Document | |
| |
| |
| |
Example of Algorithm Description Document | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Optimal Approaches Using the Big Theorems | |
| |
| |
| |
Introduction | |
| |
| |
| |
The Big Theorems | |
| |
| |
| |
Optimal Algorithms for the Linear Model | |
| |
| |
| |
Using the Theorems to Derive a New Result | |
| |
| |
| |
Practically Optimal Approaches | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Some Insights into Parameter Estimation | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Specific Algorithms | |
| |
| |
| |
Algorithms for Estimation | |
| |
| |
| |
Introduction | |
| |
| |
| |
Extracting Signal Information | |
| |
| |
| |
Enhancing Signals Corrupted by Noise/Interference | |
| |
| |
References | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Algorithms for Detection | |
| |
| |
| |
Introduction | |
| |
| |
| |
Signal with Known Form (Known Signal) | |
| |
| |
| |
Signal with Unknown Form (Random Signals) | |
| |
| |
| |
Signal with Unknown Parameters | |
| |
| |
References | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Spectral Estimation | |
| |
| |
| |
Introduction | |
| |
| |
| |
Nonparametric (Fourier) Methods | |
| |
| |
| |
Parametric (Model-Based) Spectral Analysis | |
| |
| |
| |
Time-Varying Power Spectral Densities | |
| |
| |
References | |
| |
| |
| |
Fourier Spectral Analysis and Filtering | |
| |
| |
| |
The Issue of Zero Padding and Resolution | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Real-World Extensions | |
| |
| |
| |
Complex Data Extensions | |
| |
| |
| |
Introduction | |
| |
| |
| |
Complex Signals | |
| |
| |
| |
Complex Noise | |
| |
| |
| |
Complex Least Squares and the Linear Model | |
| |
| |
| |
Algorithm Extensions for Complex Data | |
| |
| |
| |
Other Extensions | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Real-World Applications | |
| |
| |
| |
Case Studies - Estimation Problem | |
| |
| |
| |
Introduction | |
| |
| |
| |
Estimation Problem - Radar Doppler Center Frequency | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
3 dB Bandwidth of AR PSD | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Case Studies - Detection Problem | |
| |
| |
| |
Introduction | |
| |
| |
| |
Detection Problem - Magnetic Signal Detection | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Case Studies - Spectral Estimation Problem | |
| |
| |
| |
Introduction | |
| |
| |
| |
Extracting the Muscle Noise | |
| |
| |
| |
Spectral Analysis of Muscle Noise | |
| |
| |
| |
Enhancing the ECG Waveform | |
| |
| |
| |
Lessons Learned | |
| |
| |
References | |
| |
| |
| |
Solutions to Exercises | |
| |
| |
| |
Glossary of Symbols and Abbreviations | |
| |
| |
| |
Symbols | |
| |
| |
| |
Abbreviations | |
| |
| |
| |
Brief Introduction to MATLAB | |
| |
| |
| |
Overview of MATLAB | |
| |
| |
| |
Plotting in MATLAB | |
| |
| |
| |
Description of CD Contents | |
| |
| |
| |
CD Folders | |
| |
| |
| |
Utility Files Description | |
| |
| |
Index | |