»
Probability and Random Processes

# Probability and Random Processes, 2nd Edition

## With Applications to Signal Processing and Communications

9780123869814

9780123870131

560

235 X 191

The authors have focussed on creating a more level presentation and have developed more pertinent applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course

### Print Book + eBook

USD 107.94
USD 179.90

Buy both together and save 40%

Select format

### Print Book

Hardcover

In Stock

Estimated Delivery Time
USD 89.95

### eBookeBook Overview

VST (VitalSource Bookshelf) format

PDF format

USD 89.95

## Key Features

• 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

## 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.

Graduate-level courses in the topic with secondary interest to professionals

### Scott Miller

Affiliations and Expertise

Texas A & M University

Probability and Random Processes, 2nd Edition

Preface

CHAPTER 1. Introduction

1.1 A Speech Recognition System

1.3 A Communication Network

CHAPTER 2. Introduction to Probability Theory

2.1 Experiments, Sample Spaces, and Events

2.2 Axioms of Probability

2.3 Assigning Probabilities

2.4 Joint and Conditional Probabilities

2.5 Basic Combinatorics

2.6 Bayes’s Theorem

2.7 Independence

2.8 Discrete Random Variables

2.9 Engineering Application—An Optical Communication System

CHAPTER 3. Random Variables, Distributions, and Density Functions

3.1 The Cumulative Distribution Function

3.2 The Probability Density Function

3.3 The Gaussian Random Variable

3.4 Other Important Random Variables

3.5 Conditional Distribution and Density Functions

3.6 Engineering Application: Reliability and Failure Rates

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 Probability-Generating Functions

4.9 Moment-Generating 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

6.1 Joint and Conditional PMFs, CDFs, and PDFs

6.2 Expectations Involving Multiple Random Variables

6.3 Gaussian Random Variables in Multiple Dimensions

6.4 Transformations Involving Multiple Random Variables

6.5 Estimation and Detection

6.6 Engineering Application: Linear Prediction of Speech

CHAPTER 7. Random Sums and Sequences

7.1 Independent and Identically Distributed Random Variables

7.2 Convergence Modes of Random Sequences

7.3 The Law of Large Numbers

7.4 The Central Limit Theorem

7.5 Confidence Intervals

7.6 Random Sums of Random Variables

7.7 Engineering Application: A Radar System

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

10.1 Definition of PSD

10.2 The Wiener–Khintchine–Einstein Theorem

10.3 Bandwidth of a Random Process

10.4 Spectral Estimation

10.5 Thermal Noise

10.6 Engineering Application: PSDs of Digital Modulation Formats

CHAPTER 11. Random Processes in Linear Systems

11.1 Continuous Time Linear Systems

11.2 Discrete-Time Linear Systems

11.3 Noise Equivalent Bandwidth

11.4 Signal-to-Noise 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

12.1 Computer Generation of Random Variables

12.2 Generation of Random Processes

12.3 Simulation of Rare Events

12.4 Engineering Application: Simulation of a Coded Digital Communication System

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

Continuous Random Variables

Discrete Random Variables

APPENDIX E. Mathematical Tables

A. Trigonometric Identities

B. Series Expansions

C. Some Common Indefinite Integrals

D. Some Common Definite Integrals

E. Definitions of Some Common Continuous Time Signals

F. Fourier Transforms

G. z-Transforms

H. Laplace Transforms

I. Table of the Q-function

APPENDIX F. Numerical Methods for Evaluating the Q-Function

Index

#### Quotes and reviews

"...a utilitarian toolkit, to help the reader learn how to solve problems, while skirting technical issues such as measure theory…fills a particular niche in the literature, and is certainly recommended by me." --MathSciNet

"...primarily focused toward undergraduate students in areas of electrical and computer engineering...the book is very well written and wasy to read and follow." --Ali Esmaili, in TECHNOMETRICS, VOL. 47, 2005

"...very well written...I think this is a highly valuable textbook that is very recommendable for students, researchers as well as practitioners interested in signal processing and communications." --Stefan Reh, Carnegie Mellon University

"...it is well written, providing the intended readership with tools and methods to study and solve problems concerning random signals and systems." --Evelyn Buckwar, Zentralblatt MATH Berlin

"Electrical and computer engineers Miller (Texas A&M U.) and Childers (emeritus, U. of Florida) present a textbook for an upper-division undergraduate course in probability, or an introductory graduate course in random processes within an electrical engineering curriculum. Students are assumed to have the background appropriate to those levels. The area is primarily mathematical, but they treat the mathematics as a tool for engineers rather than a rigorous or elegant entity in its own right. They seek a balance between explaining elementary concepts clearly and providing enough depth that students can study modern communications systems, control systems, signal processing techniques, and other applications." --Reference and Research Book News, Inc.

Shop with Confidence

Free Shipping around the world