Table of Contents

INTRODUCTION
General Philosophy
Detection and Estimation Philosophy
Description of Spaces involved in the Decision
Summary
REVIEW OF DETERMINISTIC AND RANDOM SYSTEM AND SIGNAL CONCEPTS
Some Mathematical and Statistical Background
Systems and Signals (Deterministic and Random)
Transformation of Random Variables
Summary
INTRODUCTION TO SIGNAL PROCESSING
Introduction
Data Structure and Sampling
Discrete-Time Transformations
Filtering
Finite Impulse Response Filter
The Fast Fourier Transform
Fast Correlation
Periodogram (Power Spectral Density Estimate)
Wavelets
Summary
HYPOTHESIS TESTING
Introduction
Bayes Detection
Maximum A Posteriori (MAP) Detection
Maximum Likelihood (ML) Criterion
Minimum Probability of Error Criterion
Min-Max Criterion
Neyman-Pearson Criterion
Multiple Hypothesis Testing
Composite Hypothesis Testing
Receiver Operator Characteristic Curves and Performance
Summary
NON-PARAMETRIC AND SEQUENTIAL LIKELIHOOD RATIO DETECTORS
Introduction
Non-Parametric Detection
Wilcoxon Detector
Sequential Detection
Summary
DETECTION OF SIGNALS IN GAUSSIAN WHITE NOISE
Introduction
The Binary Detection Problem
Matched Filters
Matched Filter Approach
M-ary Communication Systems
Detection of Signals with Random Parameters
Multiple Pulse Detection
Summary
DETECTION OF SIGNALS IN COLORED GAUSSIAN NOISE
Introduction
Series Representation
Derivation of the Correlator Structure Using an Arbitrary Complete Ortho-Normal (C.O.N.) Set
Gram-Schmidt Procedure
Detection of a Known Signal in Additive White Gaussian Noise Using the Gram-Schmidt Procedure
Series Expansion for Continuous Time Detection for Colored Gaussian Noise
Detection of Known Signals in Additive Colored Gaussian Noise
Discrete Time Detection - Known Signals Embedded in Colored Gaussian Noise
Summary
ESTIMATION
Introduction
Basic Estimation Schemes
Properties of Estimators
Cramer-Rao Bound
Waveform Estimation
Summary
APPLICATIONS TO DETECTION, PARAMETER ESTIMATION, AND CLASSIFICATION
Introduction
The Periodogram and the Spectrogram
Correlation
Instantaneous Correlation Function, Wignerville Distribution, Spectral Correlation, and the Ambiguity Function
Cyclo-Stationary Processing
Higher Order Moments and Poly-Spectra
Coherence Processing
Wavelet Processing
Adaptive Techniques
Summary
APPENDICES
Probability, Random Processes and Systems
Signals and Transforms
Mathematical Structures
Some Mathematical Expressions and Moments of Probability Density Function
Wavelet Transforms
INDEX