(NOTE: Most chapters begin with an Introduction and Summary.) 1. Introduction.
(NOTE: Most chapters begin with an Introduction and Summary.) 1. Introduction.
(NOTE: Most chapters begin with an Introduction and Summary.)
1. Introduction.
Detection Theory in Signal Processing. The Detection Problem. The
Mathematical Detection Problem. Hierarchy of Detection Problems.
Role of Asymptotics. Some Notes to the Reader.
2. Summary of Important PDFs.
Fundamental Probability Density Functionshfil Penalty - M and
Properties. Quadratic Forms of Gaussian Random Variables.
Asymptotic Gaussian PDF. Monte Carlo Performance Evaluation. Number
of Required Monte Carlo Trials. Normal Probability Paper. MATLAB
Program to Compute Gaussian Right-Tail Probability and its Inverse.
MATLAB Program to Compute Central and Noncentral c 2 Right-Tail
Probability. MATLAB Program for Monte Carlo Computer
Simulation.
3. Statistical Decision Theory I.
Neyman-Pearson Theorem. Receiver Operating Characteristics.
Irrelevant Data. Minimum Probability of Error. Bayes Risk. Multiple
Hypothesis Testing. Neyman-Pearson Theorem. Minimum Bayes Risk
Detector - Binary Hypothesis. Minimum Bayes Risk Detector -
Multiple Hypotheses.
4. Deterministic Signals.
Matched Filters. Generalized Matched Filters. Multiple Signals.
Linear Model. Signal Processing Examples. Reduced Form of the
Linear Model1.
5. Random Signals.
Estimator-Correlator. Linear Model1. Estimator-Correlator for Large
Data Records. General Gaussian Detection. Signal Processing
Example. Detection Performance of the Estimator-Correlator.
6. Statistical Decision Theory II.
Composite Hypothesis Testing. Composite Hypothesis Testing
Approaches. Performance of GLRT for Large Data Records. Equivalent
Large Data Records Tests. Locally Most Powerful Detectors. Multiple
Hypothesis Testing. Asymptotically Equivalent Tests - No Nuisance
Parameters. Asymptotically Equivalent Tests - Nuisance Parameters.
Asymptotic PDF of GLRT. Asymptotic Detection Performance of LMP
Test. Alternate Derivation of Locally Most Powerful Test.
Derivation of Generalized ML Rule.
7. Deterministic Signals with Unknown Parameters.
Signal Modeling and Detection Performance. Unknown Amplitude.
Unknown Arrival Time. Sinusoidal Detection. Classical Linear Model.
Signal Processing Examples. Asymptotic Performance of the Energy
Detector. Derivation of GLRT for Classical Linear Model.
8. Random Signals with Unknown Parameters.
Incompletely Known Signal Covariance. Large Data Record
Approximations. Weak Signal Detection. Signal Processing Example.
Derivation of PDF for Periodic Gaussian Random Process.
9. Unknown Noise Parameters.
General Considerations. White Gaussian Noise. Colored WSS Gaussian
Noise. Signal Processing Example. Derivation of GLRT for Classical
Linear Model for s 2 Unknown. Rao Test for General Linear Model
with Unknown Noise Parameters. Asymptotically Equivalent Rao Test
for Signal Processing Example.
10. NonGaussian Noise.
NonGaussian Noise Characteristics. Known Deterministic Signals.
Deterministic Signals with Unknown Parameters. Signal Processing
Example. Asymptotic Performance of NP Detector for Weak Signals.
BRao Test for Linear Model Signal with IID NonGaussian Noise.
11. Summary of Detectors.
Detection Approaches. Linear Model. Choosing a Detector. Other
Approaches and Other Texts.
12. Model Change Detection.
Description of Problem. Extensions to the Basic Problem. Multiple
Change Times. Signal Processing Examples. General Dynamic
Programming Approach to Segmentation. MATLAB Program for Dynamic
Programming.
13. Complex/Vector Extensions, and Array Processing.
Known PDFs. PDFs with Unknown Parameters. Detectors for Vector
Observations. Estimator-Correlator for Large Data Records. Signal
Processing Examples. PDF of GLRT for Complex Linear Model. Review
of Important Concepts. Random Processes and Time Series Modeling.
STEVEN M. KAY is Professor of Electrical Engineering at the University of Rhode Island and a leading expert in signal processing.
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