Efnisyfirlit

• Cover Image
• Table of Contents
• Title
• Copyright
• 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
• APPENDIX E. Mathematical Tables
• APPENDIX F. Numerical Methods for Evaluating the Q-Function
• Index