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
