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Probability and Random Processes, 2nd Edition

Book Description

Miller and Childers have focused on creating a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It is aimed at graduate students as well as practicing engineers, and includes unique chapters on narrowband random processes and simulation techniques.

The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Probability and Random Processes also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields.

* Exceptional exposition and numerous worked out problems make the book extremely readable and accessible
* The authors connect the applications discussed in class to the textbook
* The new edition contains more real world signal processing and communications applications
* Includes an entire chapter devoted to simulation techniques

Table of Contents

  1. Cover Image
  2. Table of Contents
  3. Title
  4. Copyright
  5. Preface
  6. Chapter 1. Introduction
    1. 1.1 A Speech Recognition System
    2. 1.2 A Radar System
    3. 1.3 A Communication Network
  7. Chapter 2. Introduction to Probability Theory
    1. 2.1 Experiments, Sample Spaces, and Events
    2. 2.2 Axioms of Probability
    3. 2.3 Assigning Probabilities
    4. 2.4 Joint and Conditional Probabilities
    5. 2.5 Basic Combinatorics
    6. 2.6 Bayes's Theorem
    7. 2.7 Independence
    8. 2.8 Discrete Random Variables
    9. 2.9 Engineering Application—An Optical Communication System
  8. Chapter 3. Random Variables, Distributions, and Density Functions
    1. 3.1 The Cumulative Distribution Function
    2. 3.2 The Probability Density Function
    3. 3.3 The Gaussian Random Variable
    4. 3.4 Other Important Random Variables
    5. 3.5 Conditional Distribution and Density Functions
    6. 3.6 Engineering Application: Reliability and Failure Rates
  9. Chapter 4. Operations on a Single Random Variable
    1. 4.1 Expected Value of a Random Variable
    2. 4.2 Expected Values of Functions of Random Variables
    3. 4.3 Moments
    4. 4.4 Central Moments
    5. 4.5 Conditional Expected Values
    6. 4.6 Transformations of Random Variables
    7. 4.7 Characteristic Functions
    8. 4.8 Probability-Generating Functions
    9. 4.9 Moment-Generating Functions
    10. 4.10 Evaluating Tail Probabilities
    11. 4.11 Engineering Application—Scalar Quantization
    12. 4.12 Engineering Application—Entropy and Source Coding
  10. Chapter 5. Pairs of Random Variables
    1. 5.1 Joint Cumulative Distribution Functions
    2. 5.2 Joint Probability Density Functions
    3. 5.3 Joint Probability Mass Functions
    4. 5.4 Conditional Distribution, Density, and Mass Functions
    5. 5.5 Expected Values Involving Pairs of Random Variables
    6. 5.6 Independent Random Variables
    7. 5.7 Jointly Gaussian Random Variables
    8. 5.8 Joint Characteristic and Related Functions
    9. 5.9 Transformations of Pairs of Random Variables
    10. 5.10 Complex Random Variables
    11. 5.11 Engineering Application: Mutual Information, Channel Capacity, and Channel Coding
  11. Chapter 6. Multiple Random Variables
    1. 6.1 Joint and Conditional PMFs, CDFs, and PDFs
    2. 6.2 Expectations Involving Multiple Random Variables
    3. 6.3 Gaussian Random Variables in Multiple Dimensions
    4. 6.4 Transformations Involving Multiple Random Variables
    5. 6.5 Estimation and Detection
    6. 6.6 Engineering Application: Linear Prediction of Speech
  12. Chapter 7. Random Sums and Sequences
    1. 7.1 Independent and Identically Distributed Random Variables
    2. 7.2 Convergence Modes of Random Sequences
    3. 7.3 The Law of Large Numbers
    4. 7.4 The Central Limit Theorem
    5. 7.5 Confidence Intervals
    6. 7.6 Random Sums of Random Variables
    7. 7.7 Engineering Application: A Radar System
  13. Chapter 8. Random Processes
    1. 8.1 Definition and Classification of Processes
    2. 8.2 Mathematical Tools for Studying Random Processes
    3. 8.3 Stationary and Ergodic Random Processes
    4. 8.4 Properties of the Autocorrelation Function
    5. 8.5 Gaussian Random Processes
    6. 8.6 Poisson Processes
    7. 8.7 Engineering Application—Shot Noise in a p–n Junction Diode
  14. Chapter 9. Markov Processes
    1. 9.1 Definition and Examples of Markov Processes
    2. 9.2 Calculating Transition and State Probabilities in Markov Chains
    3. 9.3 Characterization of Markov Chains
    4. 9.4 Continuous Time Markov Processes
    5. 9.5 Engineering Application: A Computer Communication Network
    6. 9.6 Engineering Application: A Telephone Exchange
  15. Chapter 10. Power Spectral Density
    1. 10.1 Definition of PSD
    2. 10.2 The Wiener–Khintchine–Einstein Theorem
    3. 10.3 Bandwidth of a Random Process
    4. 10.4 Spectral Estimation
    5. 10.5 Thermal Noise
    6. 10.6 Engineering Application: PSDs of Digital Modulation Formats
  16. Chapter 11. Random Processes in Linear Systems
    1. 11.1 Continuous Time Linear Systems
    2. 11.2 Discrete-Time Linear Systems
    3. 11.3 Noise Equivalent Bandwidth
    4. 11.4 Signal-to-Noise Ratios
    5. 11.5 The Matched Filter
    6. 11.6 The Wiener Filter
    7. 11.7 Bandlimited and Narrowband Random Processes
    8. 11.8 Complex Envelopes
    9. 11.9 Engineering Application: An Analog Communication System
  17. Chapter 12. Simulation Techniques
    1. 12.1 Computer Generation of Random Variables
    2. 12.2 Generation of Random Processes
    3. 12.3 Simulation of Rare Events
    4. 12.4 Engineering Application: Simulation of a Coded Digital Communication System
  18. APPENDIX A. Review of Set Theory
  19. APPENDIX B. Review of Linear Algebra
  20. APPENDIX C. Review of Signals and Systems
  21. APPENDIX D. Summary of Common Random Variables
  22. APPENDIX E. Mathematical Tables
  23. APPENDIX F. Numerical Methods for Evaluating the Q-Function
  24. Index