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
 Cover Image
 Table of Contents
 Title
 Copyright
 Preface
 Chapter 1. Introduction
 Chapter 2. Introduction to Probability Theory
 Chapter 3. Random Variables, Distributions, and Density Functions

Chapter 4. Operations on a Single Random Variable
 4.1 Expected Value of a Random Variable
 4.2 Expected Values of Functions of Random Variables
 4.3 Moments
 4.4 Central Moments
 4.5 Conditional Expected Values
 4.6 Transformations of Random Variables
 4.7 Characteristic Functions
 4.8 ProbabilityGenerating Functions
 4.9 MomentGenerating Functions
 4.10 Evaluating Tail Probabilities
 4.11 Engineering Application—Scalar Quantization
 4.12 Engineering Application—Entropy and Source Coding

Chapter 5. Pairs of Random Variables
 5.1 Joint Cumulative Distribution Functions
 5.2 Joint Probability Density Functions
 5.3 Joint Probability Mass Functions
 5.4 Conditional Distribution, Density, and Mass Functions
 5.5 Expected Values Involving Pairs of Random Variables
 5.6 Independent Random Variables
 5.7 Jointly Gaussian Random Variables
 5.8 Joint Characteristic and Related Functions
 5.9 Transformations of Pairs of Random Variables
 5.10 Complex Random Variables
 5.11 Engineering Application: Mutual Information, Channel Capacity, and Channel Coding
 Chapter 6. Multiple Random Variables
 Chapter 7. Random Sums and Sequences

Chapter 8. Random Processes
 8.1 Definition and Classification of Processes
 8.2 Mathematical Tools for Studying Random Processes
 8.3 Stationary and Ergodic Random Processes
 8.4 Properties of the Autocorrelation Function
 8.5 Gaussian Random Processes
 8.6 Poisson Processes
 8.7 Engineering Application—Shot Noise in a p–n Junction Diode

Chapter 9. Markov Processes
 9.1 Definition and Examples of Markov Processes
 9.2 Calculating Transition and State Probabilities in Markov Chains
 9.3 Characterization of Markov Chains
 9.4 Continuous Time Markov Processes
 9.5 Engineering Application: A Computer Communication Network
 9.6 Engineering Application: A Telephone Exchange
 Chapter 10. Power Spectral Density

Chapter 11. Random Processes in Linear Systems
 11.1 Continuous Time Linear Systems
 11.2 DiscreteTime Linear Systems
 11.3 Noise Equivalent Bandwidth
 11.4 SignaltoNoise Ratios
 11.5 The Matched Filter
 11.6 The Wiener Filter
 11.7 Bandlimited and Narrowband Random Processes
 11.8 Complex Envelopes
 11.9 Engineering Application: An Analog Communication System
 Chapter 12. Simulation Techniques
 APPENDIX A. Review of Set Theory
 APPENDIX B. Review of Linear Algebra
 APPENDIX C. Review of Signals and Systems
 APPENDIX D. Summary of Common Random Variables
 APPENDIX E. Mathematical Tables
 APPENDIX F. Numerical Methods for Evaluating the QFunction
 Index
Product Information
 Title: Probability and Random Processes, 2nd Edition
 Author(s):
 Release date: January 2012
 Publisher(s): Academic Press
 ISBN: 9780123869814