# Detection Theory

by Ralph D. Hippenstiel, Hippenstiel D. Hippenstiel

Continuous Signals and Systems with MATLAB is the first undergraduate text fully focused on continuous systems. It presents all of the material needed to master the subject and its related MATLAB problem-solving techniques. The authors cover all of the traditional topics and include chapters on system design, state-space techniques, linearizing nonlinear systems,

… See more details below## Overview

Continuous Signals and Systems with MATLAB is the first undergraduate text fully focused on continuous systems. It presents all of the material needed to master the subject and its related MATLAB problem-solving techniques. The authors cover all of the traditional topics and include chapters on system design, state-space techniques, linearizing nonlinear systems, and the design and analysis of analog filters. They also discuss the five representations of continuous systems and explain how to go from one representation to another.

## Product Details

- ISBN-13:
- 9780849304347
- Publisher:
- Taylor & Francis
- Publication date:
- 01/01/2002
- Edition description:
- New Edition
- Pages:
- 344
- Product dimensions:
- 6.14(w) x 9.21(h) x 0.81(d)

## 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

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