Book description
An understanding of random processes is crucial to many engineering fieldsincluding communication theory, computer vision, and digital signal processing in electrical and computer engineering, and vibrational theory and stress analysis in mechanical engineering. The filtering, estimation, and detection of random processes in noisy environments are critical tasks necessary in the analysis and design of new communications systems and useful signal processing algorithms. Random Processes: Filtering, Estimation, and Detection clearly explains the basics of probability and random processes and details modern detection and estimation theory to accomplish these tasks.
In this book, Lonnie Ludeman, an awardwinning authority in digital signal processing, joins the fundamentals of random processes with the standard techniques of linear and nonlinear systems analysis and hypothesis testing to give signal estimation techniques, specify optimum estimation procedures, provide optimum decision rules for classification purposes, and describe performance evaluation definitions and procedures for the resulting methods. The text covers four main, interrelated topics:
Probability and characterizations of random variables and random processes
Linear and nonlinear systems with random excitations
Optimum estimation theory including both the Wiener and Kalman Filters
Detection theory for both discrete and continuous time measurements
Lucid, thorough, and wellstocked with numerous examples and practice problems that emphasize the concepts discussed, Random Processes: Filtering, Estimation, and Detection is an understandable and useful text ideal as both a selfstudy guide for professionals in the field and as a core text for graduate students.
Table of contents
 Cover Page
 Title Page
 Copyright
 Dedication
 CONTENTS
 PREFACE
 Chapter 1: Experiments and Probability

Chapter 2: Random Variables
 2.1 DEFINITION OF A RANDOM VARIABLE
 2.2 COMMON CONTINUOUS RANDOM VARIABLES
 2.3 COMMON DISCRETE RANDOM VARIABLES
 2.4 TRANSFORMATIONS OF ONE RANDOM VARIABLE
 2.5 COMPUTATION OF EXPECTED VALUES
 2.6 TWO RANDOM VARIABLES
 2.7 TWO FUNCTIONS OF TWO RANDOM VARIABLES
 2.8 ONE FUNCTION OF TWO RANDOM VARIABLES
 2.9 COMPUTATION OF E [ h ( X , Y )]
 2.10 MULTIPLE RANDOM VARIABLES
 2.11 M FUNCTIONS OF N RANDOM VARIABLES
 Chapter 3: Estimation of Random Variables

Chapter 4: Random Processes
 4.1 DEFINITION OF A RANDOM PROCESS
 4.2 CHARACTERIZATIONS OF A RANDOM PROCESS
 4.3 STATIONARITY OF RANDOM PROCESSES
 4.4 EXAMPLES OF RANDOM PROCESSES
 4.5 DEFINITE INTEGRALS OF RANDOM PROCESSES
 4.6 JOINT CHARACTERIZATIONS OF RANDOM PROCESSES
 4.7 GAUSSIAN RANDOM PROCESSES
 4.8 WHITE RANDOM PROCESSES
 4.9 ARMA RANDOM PROCESSES
 4.10 PERIODIC RANDOM PROCESSES
 4.11 SAMPLING OF CONTINUOUS RANDOM PROCESSES
 4.12 ERGODIC RANDOM PROCESSES

Chapter 5: Linear Systems: Random Processes
 5.1 INTRODUCTION
 5.2 CLASSIFICATION OF SYSTEMS
 5.3 CONTINUOUS LINEAR TIMEINVARIANT SYSTEMS (RANDOM INPUTS)
 5.4 CONTINUOUS TIMEVARYING SYSTEMS WITH RANDOM INPUT
 5.5 DISCRETE TIMEINVARIANT LINEAR SYSTEMS WITH RANDOM INPUTS
 5.6 DISCRETE TIMEVARYING LINEAR SYSTEMS WITH RANDOM INPUTS
 5.7 LINEAR SYSTEM IDENTIFICATION
 5.8 DERIVATIVES OF RANDOM PROCESSES
 5.9 MULTIINPUT, MULTIOUTPUT LINEAR SYSTEMS
 5.10 TRANSIENTS IN LINEAR SYSTEMS
 5.11 SUMMARY
 Chapter 6: Nonlinear Systems: Random Processes
 Chapter 7: Optimum Linear Filters: The Wiener Approach
 Chapter 8: Optimum Linear Systems: The Kalman Approach

Chapter 9: Detection Theory: Discrete Observation
 9.1 BASIC DETECTION PROBLEM
 9.2 MAXIMUM A POSTERIORI DECISION RULE
 9.3 MINIMUM PROBABILITY OF ERROR CLASSIFIER
 9.4 BAYES DECISION RULE
 9.5 SPECIAL CASES FOR THE MULTIPLECLASS PROBLEM (BAYES)
 9.6 NEYMANPEARSON CLASSIFIER
 9.7 GENERAL CALCULATION OF PROBABILITY OF ERROR
 9.8 GENERAL GAUSSIAN PROBLEM
 9.9 COMPOSITE HYPOTHESES
 9.10 SUMMARY

Chapter 10: Detection Theory: Continuous Observation
 10.1 CONTINUOUS OBSERVATIONS
 10.2 DETECTION OF KNOWN SIGNALS IN WHITE GAUSSIAN NOISE
 10.3 DETECTION OF KNOWN SIGNALS IN NONWHITE GAUSSIAN NOISE (ANWGN)
 10.4 DETECTION OF KNOWN SIGNALS IN COMBINATION OF WHITE AND NONWHITE GAUSSIAN NOISE (AW&NWGN)
 10.5 OPTIMUM CLASSIFIER FOR GENERAL GAUSSIAN PROCESSES (TWOCLASS DETECTION)
 10.6 DETECTION OF KNOWN SIGNALS WITH RANDOM PARAMETERS IN ADDITIVE WHITE GAUSSIAN NOISE
 10.7 SUMMARY
 APPENDIX A: The Bilateral Laplace Transform
 APPENDIX B: Table of Binomial Probabilities
 APPENDIX C: Table of Discrete Random Variables and Properties
 APPENDIX D: Table of Continuous Random Variables and Properties
 APPENDIX E: Table for Gaussian Cumulative Distribution Function
 INDEX
Product information
 Title: Random Processes: Filtering, Estimation, and Detection
 Author(s):
 Release date: January 2003
 Publisher(s): WileyIEEE Press
 ISBN: 9780471259756
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