Dolecek G.J. Random Signals and Processes Primer with MatLAB

Springer, 2013. 536 p. ISBN: 1461423856This book provides anyone needing a primer on random signals and processes with a highly accessible introduction to these topics. It assumes a minimal amount of mathematical background and focuses on concepts, related terms and interesting applications to a variety of fields. All of this is motivated by numerous examples implemented with MatLAB. Provides a highly accessible introduction to the concepts and key terms related to random variables and processes;Assumes minimal mathematical background and gives simple explanations of key terms such as density, distribution, mean value, variance, correlation, autocorrelation, ergodicity, etc;Includes many examples and applications implemented in MatLABIntroduction to Sample Space and Probability
Sample Space and Events
Operations with Events
Probability of Events
Axioms
Properties
Equally Likely Outcomes in the Sample Space
Relative Frequency Definition of Probability
Conditional Probability
Total Probability and Bayes’ Rule
Total Probability
Bayes’ Rule
Independent Events
Numerical Exercises
Questions
Answers
Random Variable
What Is a Random Variable?Definition of a Random Variable
Distribution Function
Definition
Properties
Probability Density Function
Definition
Delta Function
Densities of Discrete and Mixed Random Variables
Properties
Examples of Density Functions
How to Estimate Density and Distribution in MatLAB
Density Function (MatLAB File: PDF.m)
Distribution Function (MatLAB File: Distribution.m)
Conditional Distribution and PDF
Definition of Conditional Distribution and PDF
Definition of a Conditioned Event
Transformation of a Random VariableMonotone Transformation
Nonmonotone Transformation
Transformation of Discrete Random Variables
Mean Value
What Is a Mean Value?
Concept of a Mean Value of a Discrete Random Variable
Mean Value of a Continuous Random Variable
General Expression of Mean Value for Discrete, Continuous, and Mixed Random Variables
Conditional Mean Values
Moments
Moments Around the Origin
Central Moments
Moments and PDF
Functions Which Give Moments
Chebyshev Inequality
Numerical Exercises
MatLAB Exercises
Questions
Answers
Multidimensional Random Variables
What Is a Multidimensional Random Variable?
Two-Dimensional Random Variable
Joint Distribution and Density
Joint Distribution
Joint Density Function
Conditional Distribution and Density
Independent Random Variables
Expected Values and Moments
Expected Value
Joint Moments Around the Origin
Joint Central Moments
ndependence and Correlation
Transformation of Random Variables
One-to-One Transformation
Nonunique Transformation
Generalization for N Variables
Characteristic Functions
Definition
Characteristic Function of the Sum of the Independent Variables
Moment Theorem
PDF of the Sum of Independent Random Variables
Numerical Exercises
MatLAB Exercises
Questions
Answers
Normal Random Variable
Normal PDF
Definition
Properties
Normal Distribution
Definition
Practical Calculation
The 3 s Rule
Transformation of Normal Random Variable
Monotone Transformation
Nonmonotone Transformation
How to Generate a Normal Variable in MatLAB?
Sum of Independent Normal Variables
Characteristic Function
Characteristic Function of the Sum of Independent Variables
Sum of Linear Transformations of Independent Normal Random Variables
Central Limit Theorem
Jointly Normal Variables
Two Jointly Normal Variables
N-Jointly Normal Random Variables
Summary of Properties
Numerical Exercises
MatLAB Exercises
Questions
Answers
Other Important Random Variables
Lognormal Random Variable
Density Function
Distribution Function
Moments
What Does a Lognormal Variable Tell Us?
Rayleigh Random Variable
Density Function
Distribution Function
Moments
Relation of Rayleigh and Normal Variables
Rician Random Variable
Relation of Rician, Rayleigh, and Normal Variables
Exponential Random Variable
Density and Distribution Function
Characteristic Function and Moments
Memory-Less Property
ariables Related with Exponential Variable
Laplacian Random Variable
Gamma and Erlang’s Random Variables
Weibull Random Variable
Bernoulli and Binomial Random Variables
Bernoulli Experiments
What Is a Binomial Random Variable?
Binomial Distribution and Density
Characteristic Functions and Moments
Approximation of Binomial Variable
Poisson Random Variable
Approximation of Binomial Variable
Poisson Variable as a Counting Random Variable
Distribution and Density Functions
Characteristic Function
Sum of Independent Poisson Variables
Poisson Flow of Events
Geometric Random Variable
What Is a Geometric Random Variable and Where Does This Name Come From?
Probability Distribution and Density Functions
Characteristic Functions and Moments
The Memory-Less Property of Geometric RandomVariable
Numerical Exercises
MatLAB Exercises
Questions
Answers
Random Processes
What Is aRandomProcess?
Deterministic and Nondeterministic Random Processes
Continuous and Discrete Random Processes
Statistics ofRandomProcesses
Description of a Process in One Point
Description of a Process in Two Points
Description of Process in n Points
StationaryRandomProcesses
MeanValue
Autocorrelation Function
Definition
WS Stationary Processes
What Does Autocorrelation Function Tell Us and Why Do We Need It?
Properties of Autocorrelation Function for WS Stationary Processes
Autocovariance
Cross-Correlation Function
Definition
Jointly WS Processes
Properties of Cross-Correlation Function for Jointly WS Stationary Processes
Cross-Covariance
Ergodic Processes
Time Averaging
What Is Ergodicity?
Explanation of Ergodicity
Mean Ergodic Process
Autocorrelation and Cross-Correlation Ergodic Processes
Numerical Exercises
MatLAB Exercises
Questions
Answers
Spectral Characteristics of Random Processes
Power Spectral Density
Fourier Transformation of Deterministic Signals
How to Apply the Fourier Transformation to Random Signals?
PSD and Autocorrelation Function
Properties of PSD
Interpretation of PSD
Classification of Processes
Low-Pass, Band-Pass, Band-Limited, and Narrow-Band Processes
White and Colored Processes
Nonzero Mean Process
Random Sinusoidal Process
Bandwidth of Random Process
Cross-Power Spectrum
Definition
Properties of Cross-Spectral Density Function
Operation of Processes
Sum of Random Processes
Multiplication of Random Process with a Sinusoidal Signal
Filtering of Random Process
Numerical Exercises
MatLAB Exercises
Questions
Answers
Appendix A: Definite Integrals
Appendix B: Indefinite Integrals
Appendix C: Gamma Function
Appendix D: Useful Mathematical Quantities
Appendix E: Fourier Transform