Probability and Random Processes, 2nd ed. by Scott Miller & Donald Childers
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Description
Probability and Random Processes, Second Edition presents pertinent applications to signal processing and communications, two areas of key interest to students and professionals in today's booming communications industry. The book includes unique chapters on narrowband random processes and simulation techniques. It also describes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and others.
Exceptional exposition and numerous worked out problems make this 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. It introduces the reader to the basics of probability theory and explores topics ranging from random variables, distributions and density functions to operations on a single random variable. There are also discussions on pairs of random variables; multiple random variables; random sequences and series; random processes in linear systems; Markov processes; and power spectral density. View more >
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
Readership
Graduate-level courses in the topic with secondary interest to professionals
Table of Contents
Preface
CHAPTER 1. Introduction
1.1 A Speech Recognition System
1.2 A Radar 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 View less >
Details
No. of pages:
522
Language:
English
Copyright:
© Academic Press 2012
Published:
11th January 2012
Imprint:
Academic Press
eBook ISBN:
9780123870131
Probability and Random Processes, Second Edition presents pertinent applications to signal processing and communications, two areas of key interest to students and professionals in today's booming communications industry. The book includes unique chapters on narrowband random processes and simulation techniques. It also describes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and others.
Exceptional exposition and numerous worked out problems make this 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. It introduces the reader to the basics of probability theory and explores topics ranging from random variables, distributions and density functions to operations on a single random variable. There are also discussions on pairs of random variables; multiple random variables; random sequences and series; random processes in linear systems; Markov processes; and power spectral density. View more >
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
Readership
Graduate-level courses in the topic with secondary interest to professionals
Table of Contents
Preface
CHAPTER 1. Introduction
1.1 A Speech Recognition System
1.2 A Radar 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 View less >
Details
No. of pages:
522
Language:
English
Copyright:
© Academic Press 2012
Published:
11th January 2012
Imprint:
Academic Press
eBook ISBN:
9780123870131