1st Edition

Detection Theory Applications and Digital Signal Processing

By Ralph D. Hippenstiel Copyright 2002

    Using simplified notation and a practical approach, Detection Theory: Applications and Digital Signal Processing introduces the principles of detection theory, the necessary mathematics, and basic signal processing methods along with some recently developed statistical techniques. Throughout the book, the author keeps the needs of practicing engineers firmly in mind. His presentation and choice of topics allows students to quickly become familiar with the detection and signal processing fields and move on to more advanced study and practice. The author also presents many applications and wide-ranging examples that demonstrate how to apply the concepts to real-world problems.

    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

    Biography

    Ralph D. Hippenstiel