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Random Processes: Filtering, Estimation, and Detection

Book Description

An understanding of random processes is crucial to many engineering fields-including 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 award-winning 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 well-stocked 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 self-study guide for professionals in the field and as a core text for graduate students.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. CONTENTS
  6. PREFACE
  7. Chapter 1: Experiments and Probability
    1. 1.1 DEFINITION OF AN EXPERIMENT
    2. 1.2 COMBINED EXPERIMENTS
    3. 1.3 CONDITIONAL PROBABILITY
    4. 1.4 RANDOM POINTS
    5. 1.5 SUMMARY
  8. Chapter 2: Random Variables
    1. 2.1 DEFINITION OF A RANDOM VARIABLE
    2. 2.2 COMMON CONTINUOUS RANDOM VARIABLES
    3. 2.3 COMMON DISCRETE RANDOM VARIABLES
    4. 2.4 TRANSFORMATIONS OF ONE RANDOM VARIABLE
    5. 2.5 COMPUTATION OF EXPECTED VALUES
    6. 2.6 TWO RANDOM VARIABLES
    7. 2.7 TWO FUNCTIONS OF TWO RANDOM VARIABLES
    8. 2.8 ONE FUNCTION OF TWO RANDOM VARIABLES
    9. 2.9 COMPUTATION OF E [ h ( X , Y )]
    10. 2.10 MULTIPLE RANDOM VARIABLES
    11. 2.11 M FUNCTIONS OF N RANDOM VARIABLES
  9. Chapter 3: Estimation of Random Variables
    1. 3.1 ESTIMATION OF VARIABLES
    2. 3.2 LINEAR MMSE ESTIMATION
    3. 3.3 NONLINEAR MMSE ESTIMATION
    4. 3.4 PROPERTIES OF ESTIMATORS OF RANDOM VARIABLES
    5. 3.5 BAYES ESTIMATION
    6. 3.6 ESTIMATION OF NONRANDOM PARAMETERS
    7. 3.7 SUMMARY
  10. Chapter 4: Random Processes
    1. 4.1 DEFINITION OF A RANDOM PROCESS
    2. 4.2 CHARACTERIZATIONS OF A RANDOM PROCESS
    3. 4.3 STATIONARITY OF RANDOM PROCESSES
    4. 4.4 EXAMPLES OF RANDOM PROCESSES
    5. 4.5 DEFINITE INTEGRALS OF RANDOM PROCESSES
    6. 4.6 JOINT CHARACTERIZATIONS OF RANDOM PROCESSES
    7. 4.7 GAUSSIAN RANDOM PROCESSES
    8. 4.8 WHITE RANDOM PROCESSES
    9. 4.9 ARMA RANDOM PROCESSES
    10. 4.10 PERIODIC RANDOM PROCESSES
    11. 4.11 SAMPLING OF CONTINUOUS RANDOM PROCESSES
    12. 4.12 ERGODIC RANDOM PROCESSES
  11. Chapter 5: Linear Systems: Random Processes
    1. 5.1 INTRODUCTION
    2. 5.2 CLASSIFICATION OF SYSTEMS
    3. 5.3 CONTINUOUS LINEAR TIME-INVARIANT SYSTEMS (RANDOM INPUTS)
    4. 5.4 CONTINUOUS TIME-VARYING SYSTEMS WITH RANDOM INPUT
    5. 5.5 DISCRETE TIME-INVARIANT LINEAR SYSTEMS WITH RANDOM INPUTS
    6. 5.6 DISCRETE TIME-VARYING LINEAR SYSTEMS WITH RANDOM INPUTS
    7. 5.7 LINEAR SYSTEM IDENTIFICATION
    8. 5.8 DERIVATIVES OF RANDOM PROCESSES
    9. 5.9 MULTI-INPUT, MULTI-OUTPUT LINEAR SYSTEMS
    10. 5.10 TRANSIENTS IN LINEAR SYSTEMS
    11. 5.11 SUMMARY
  12. Chapter 6: Nonlinear Systems: Random Processes
    1. 6.1 INTRODUCTION
    2. 6.2 CLASSIFICATION OF NONLINEAR SYSTEMS
    3. 6.3 RANDOM OUTPUTS FOR INSTANTANEOUS NONLINEAR SYSTEMS
    4. 6.4 CHARACTERIZATIONS FOR BILINEAR SYSTEMS
    5. 6.5 CHARACTERIZATIONS FOR TRILINEAR SYSTEMS
    6. 6.6 CHARACTERIZATIONS FOR VOLTERRA NONLINEAR SYSTEMS
    7. 6.7 HIGHER-ORDER CHARACTERIZATIONS
    8. 6.8 SUMMARY
  13. Chapter 7: Optimum Linear Filters: The Wiener Approach
    1. 7.1 OPTIMUM FILTER FORMULATION
    2. 7.2 BASIC PROBLEMS
    3. 7.3 THE WIENER FILTER
    4. 7.4 THE DISCRETE WIENER FILTER
    5. 7.5 OPTIMAL LINEAR SYSTEM OF PARAMETRIC FORM
    6. 7.6 SUMMARY
  14. Chapter 8: Optimum Linear Systems: The Kalman Approach
    1. 8.1 INTRODUCTION
    2. 8.2 DISCRETE TIME SYSTEMS
    3. 8.3 BASIC ESTIMATION PROBLEM
    4. 8.4 OPTIMAL FILTERED ESTIMATE
    5. 8.5 OPTIMAL PREDICTION
    6. 8.6 OPTIMAL SMOOTHING
    7. 8.7 STEADY STATE EQUIVALENCE OF THE KALMAN AND WIENER FILTERS
    8. 8.8 SUMMARY
  15. Chapter 9: Detection Theory: Discrete Observation
    1. 9.1 BASIC DETECTION PROBLEM
    2. 9.2 MAXIMUM A POSTERIORI DECISION RULE
    3. 9.3 MINIMUM PROBABILITY OF ERROR CLASSIFIER
    4. 9.4 BAYES DECISION RULE
    5. 9.5 SPECIAL CASES FOR THE MULTIPLE-CLASS PROBLEM (BAYES)
    6. 9.6 NEYMAN-PEARSON CLASSIFIER
    7. 9.7 GENERAL CALCULATION OF PROBABILITY OF ERROR
    8. 9.8 GENERAL GAUSSIAN PROBLEM
    9. 9.9 COMPOSITE HYPOTHESES
    10. 9.10 SUMMARY
  16. Chapter 10: Detection Theory: Continuous Observation
    1. 10.1 CONTINUOUS OBSERVATIONS
    2. 10.2 DETECTION OF KNOWN SIGNALS IN WHITE GAUSSIAN NOISE
    3. 10.3 DETECTION OF KNOWN SIGNALS IN NONWHITE GAUSSIAN NOISE (ANWGN)
    4. 10.4 DETECTION OF KNOWN SIGNALS IN COMBINATION OF WHITE AND NONWHITE GAUSSIAN NOISE (AW&NWGN)
    5. 10.5 OPTIMUM CLASSIFIER FOR GENERAL GAUSSIAN PROCESSES (TWO-CLASS DETECTION)
    6. 10.6 DETECTION OF KNOWN SIGNALS WITH RANDOM PARAMETERS IN ADDITIVE WHITE GAUSSIAN NOISE
    7. 10.7 SUMMARY
  17. APPENDIX A: The Bilateral Laplace Transform
  18. APPENDIX B: Table of Binomial Probabilities
  19. APPENDIX C: Table of Discrete Random Variables and Properties
  20. APPENDIX D: Table of Continuous Random Variables and Properties
  21. APPENDIX E: Table for Gaussian Cumulative Distribution Function
  22.     INDEX