Random Signals for Engineers Using MATLAB® and Mathcad®

1 Introduction to Sets and Probability.- 1.1 Introduction to Nondeterministic Signals.- 1.2 Introduction to Sets.- 1.3 Operations on Sets.- 1.4 Combined Operations on Sets.- 1.5 Notion of Probability.- 1.6 Relative Frequency and Probability.- 1.7 Conditional Probability.- 1.8 Total Probability.- 1.9 Independence.- 1.10 Summary.- Problems for Chapter 1.- 2 One-Dimensional Random Variables.- 2.1 Concept of Distributions.- 2.2 Random Variables.- 2.3 Distribution Functions.- 2.4 Density Functions.- 2.5 Continuous Density Functions.- 2.6 Conditional Distribution and Density Functions.- 2.7 Generation of Random Numbers.- 2.8 Summary.- Problems for Chapter 2.- 3 Operations on Random Numbers.- 3.1 Concept of Expectation.- 3.2 Moments and Functions.- 3.3 Moment Generating Functions.- 3.4 Transformation of Random Variables.- 3.5 Random Variables with Prescribed Distributions.- 3.6 Summary.- Problems for Chapter 3.- 4 Two-Dimensional Random Variables.- 4.1 Joint Distribution and Density Functions.- 4.2 Conditional Density Functions.- 4.3 Expectation and Joint Moments.- 4.4 Transformations and Joint Characteristic Functions.- 4.5 Independence.- 4.6 Sum of Independent Random Variables.- 4.7 Generation of Correlated Gaussian Random Sequences.- 4.8 Summary.- Problems for Chapter 4.- 5 Introduction to Random Processes.- 5.1 Methods of Generation of Random Processes.- 5.2 IID Random Variables.- 5.3 Distribution Functions for a Random Process.- 5.4 Properties of Expectation Operators.- 5.5 Properties of the Correlation Functions.- 5.6 Numerical Computation of the Correlation Function.- 5.7 Summary.- Problems for Chapter 5.- 6 Introduction to Transformations.- 6.1 Function Transformation of Random Processes.- 6.2 Transformation by Integration.- 6.3 Transformation by Differentiation.- 6.4Linear Systems.- 6.5 Power Spectrum Functions.- 6.6 Transforms of Linear Systems.- 6.7 Calculation of Power Density Spectrum.- 6.8 Summary.- Problems for Chapter 6.- 7 Introduction to Applications.- 7.1 Matched Filtering.- 7.2 Mean Square Filtering.- 7.3 Detection Theory.- 7.4 Radar Systems.- 7.5 Noise in Control Systems.- Problems for Chapter 7.- Appendix A.- A.l Signals and Spectra.- A.2 Singularity Functions.- A.3 Linear-Time-Invariant Systems.- A.4 Correlation Functions.- Appendix B.- B.1 Matlab and Mathcad.- B.2 Matlab.- B.3 Mathcad.- B.4 Contents of the CD-ROM.- References.