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| Introduction | |
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| Detection Theory in Signal Processing | |
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| The Detection Problem | |
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| The Mathematical Detection Problem | |
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| Hierarchy of Detection Problems | |
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| Role of Asymptotics | |
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| Some Notes to the Reader | |
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| Summary of Important PDFs | |
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| Fundamental Probability Density Functionshfil Penalty - M and Properties | |
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| Quadratic Forms of Gaussian Random Variables | |
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| Asymptotic Gaussian PDF | |
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| Monte Carlo Performance Evaluation | |
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| Number of Required Monte Carlo Trials | |
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| Normal Probability Paper | |
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| MATLAB Program to Compute Gaussian Right-Tail Probability and its Inverse | |
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| MATLAB Program to Compute Central and Noncentral c 2 Right-Tail Probability | |
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| MATLAB Program for Monte Carlo Computer Simulation | |
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| Statistical Decision Theory I | |
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| Neyman-Pearson Theorem | |
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| Receiver Operating Characteristics | |
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| Irrelevant Data | |
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| Minimum Probability of Error | |
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| Bayes Risk | |
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| Multiple Hypothesis Testing | |
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| Neyman-Pearson Theorem | |
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| Minimum Bayes Risk Detector - Binary Hypothesis | |
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| Minimum Bayes Risk Detector - Multiple Hypotheses | |
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| Deterministic Signals | |
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| Matched Filters | |
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| Generalized Matched Filters | |
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| Multiple Signals | |
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| Linear Model | |
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| Signal Processing Examples | |
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| Reduced Form of the Linear Model1 | |
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| Random Signals | |
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| Estimator-Correlator | |
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| Linear Model1 | |
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| Estimator-Correlator for Large Data Records | |
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| General Gaussian Detection | |
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| Signal Processing Example | |
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| Detection Performance of the Estimator-Correlator | |
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| Statistical Decision Theory II | |
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| Composite Hypothesis Testing | |
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| Composite Hypothesis Testing Approaches | |
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| Performance of GLRT for Large Data Records | |
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| Equivalent Large Data Records Tests | |
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| Locally Most Powerful Detectors | |
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| Multiple Hypothesis Testing | |
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| Asymptotically Equivalent Tests - No Nuisance Parameters | |
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| Asymptotically Equivalent Tests - Nuisance Parameters | |
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| Asymptotic PDF of GLRT | |
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| Asymptotic Detection Performance of LMP Test | |
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| Alternate Derivation of Locally Most Powerful Test | |
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| Derivation of Generalized ML Rule | |
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| Deterministic Signals with Unknown Parameters | |
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| Signal Modeling and Detection Performance | |
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| Unknown Amplitude | |
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| Unknown Arrival Time | |
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| Sinusoidal Detection | |
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| Classical Linear Model | |
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| Signal Processing Examples | |
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| Asymptotic Performance of the Energy Detector | |
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| Derivation of GLRT for Classical Linear Model | |
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| Random Signals with Unknown Parameters | |
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| Incompletely Known Signal Covariance | |
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| Large Data Record Approximations | |
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| Weak Signal Detection | |
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| Signal Processing Example | |
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| Derivation of PDF for Periodic Gaussian Random Process | |
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| Unknown Noise Parameters | |
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| General Considerations | |
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| White Gaussian Noise | |
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| Colored WSS Gaussian Noise | |
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| Signal Processing Example | |
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| Derivation of GLRT for Classical Linear Model for s 2 Unknown | |
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| Rao Test for General Linear Model with Unknown Noise Parameters | |
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| Asymptotically Equivalent Rao Test for Signal Processing Example | |
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| NonGaussian Noise | |
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| NonGaussian Noise Characteristics | |
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| Known Deterministic Signals | |
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| Deterministic Signals with Unknown Parameters | |
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| Signal Processing Example | |
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| Asymptotic Performance of NP Detector for Weak Signals | |
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| BRao Test for Linear Model Signal with IID NonGaussian Noise | |
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| Summary of Detectors | |
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| Detection Approaches | |
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| Linear Model | |
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| Choosing a Detector | |
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| Other Approaches and Other Texts | |
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| Model Change Detection | |
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| Description of Problem | |
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| Extensions to the Basic Problem | |
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| Multiple Change Times | |
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| Signal Processing Examples | |
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| General Dynamic Programming Approach to Segmentation | |
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| MATLAB Program for Dynamic Programming | |
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| Complex/Vector Extensions, and Array Processing | |
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| Known PDFs | |
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| PDFs with Unknown Parameters | |
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| Detectors for Vector Observations | |
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| Estimator-Correlator for Large Data Records | |