Probabilistic Methods of Signal and System Analysis

Preface ; 1. Introduction To Probability ; 1-1 Engineering Applications Of Probability ; 1-2 Random Experiments And Events ; 1-3 Definitions Of Probability ; 1-4 The Relative-Frequency Approach ; 1-5 Elementary Set Theory ; 1-6 The Axiomatic Approach ; 1-7 Conditional Probability ; 1-8 Independence ; 1-9 Combined Experiments ; 1-10 Bemoulli Trials ; 1-11 Applications Of Bemoulli Trials ; 2. Random Variables ; 2-1 Concept Of A Random Variable ; 2-2 Distribution Functions ; 2-3 Density Functions ; 2-4 Mean Values And Moments ; 2-5 The Gaussian Random Variable ; 2-6 Density Functions Related To Gaussian ; 2-7 Other Probability Density Functions ; 2-8 Conditional Probability Distribution And Density Functions ; 2-9 Examples And Applications ; 3. Several Random Variables ; 3-1 Two Random Variables ; 3-2 Conditional Probability-Revisited ; 3-3 Statistical Independence ; 3-4 Correlation Between Random Variables ; 3-5 Density Function Of The Sum Of Two Random Variables ; 3-6 Probability Density Function Of A Function Of Two Random Variables ; 3-7 The Characteristic Function ; 4. Elements oOf Statistics ; 4-1 Introduction ; 4-2 Sampling Theory- The Sample Mean ; 4-3 Sampling Theory- The Sample Variance ; 4-4 Sampling Distributions And Confidence Intervals ; 4-5 Hypothesis Testing ; 4-6 Curve Fitting And Linear Regression ; 4-7 Correlation Between Two Sets of Data ; 5. Random Processes ; 5-1 Introduction ; 5-2 Continuous And Discrete Random Processes ; 5-3 Deterministic And Nondeterministic Random Processes ; 5-4 Stationary and Nonstationary Random Processes ; 5-5 Ergodic And Nonergodic Random Processes ; 5-6 Measurement Of Process Parameters ; 5-7 Smoothing Data With A Moving Window Average ; 6. Correlation Functions ; 6-1 Introduction ; 6-2 Example:Autocorrelation Function Of A Binary Profess ; 6-3 Properties Of Autocorrelation Functions ; 6-4 Measurement Of Autocorrelation Functions ; 6-5 Examples Of Autocorrelation Functions ; 6-6 Crosscorrelation Functions ; 6-7 Properties Of Crosscorrelation Functions ; 6-8 Examples And Applications Of Crosscorrelation Functions ; 6-9 Correlation Matrices For Sampled Functions ; 7. Spectral Density ; 7-1 Introduction ; 7-3 Properties Of Spectral Density ; 7-4 Spectral Density And The Complex Frequency Plane ; 7-5 Mean-Square Values From Spectral Density ; 7-6 Relation Of Spectral Density To The Autocorrelation Function ; 7-7 White Noise ; 7-8 Cross-Spectral Density ; 7-9 Measurement Of Spectral Density ; 7-10 Periodogram Estimate Of Spectral Density ; 7-11 Examples And Applications Of Spectral Density ; 8. Repines Of Linear Systems To Random Inputs ; 8-1 Introduction ; 8-2 Analysis In The Time Domain ; 8-3 Mean And Mean-Swquare Value Of System Output ; 8-4 Autocorrelation Function Of System Output ; 8-5 Crosscorrelation Between Input And Output ; 8-6 Example Of Time-Domain Analysis ; 8-7 Analysis In The Frequency Domain ; 8-8 Spectral Density At The System Output ; 8-9 Cross-Spectral Densities Between Input And Output ; 8-10 Examples Of Frequency-Domain Analysis ; 8-11 Numerical Computation Of System Output ; 9. Optimum Linear Systems ; 9-1 Introduction ; 9-2 Criteria Of Optimaility ; 9-3 Restrictions On The Optimum System ; 9-4 Optimization By Parameter Adjustment ; 9-6 Systems That Minimize Mean-Square Error ; Appendices ; Appendix A: Mathematical Tables ; Appendix B: Frequently Encountered Probability Distributions ; Appendix C: Binomial Coefficients ; Appendix D: Normal Probability Distribution Function ; Appendix E: The Q-Function ; Appendix F: Student's T-Distribution Function ; Appendix G: Computer Computations ; Appendix H: Table Of Correlation Function-Spectral Density Pairs ; Appendix I: Contour Integration