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Probabilistic Methods of Signal and System Analysis (Oxford Series in Electrical and Computer Engineering)by George R. Cooper
Synopses & ReviewsPublisher Comments:Probabilistic Methods of Signal and System Analysis, 3/e stresses the engineering applications of probability theory, presenting the material at a level and in a manner ideally suited to engineering students at the junior or senior level. It is also useful as a review for graduate students and practicing engineers.
Thoroughly revised and updated, this third edition incorporates increased use of the computer in both text examples and selected problems. It utilizes MATLAB as a computational tool and includes new sections relating to Bernoulli trials, correlation of data sets, smoothing of data, computer computation of correlation functions and spectral densities, and computer simulation of systems. All computer examples can be run using the Student Version of MATLAB. Almost all of the examples and many of the problems have been modified or changed entirely, and a number of new problems have been added. A separate appendix discusses and illustrates the application of computers to signal and system analysis. Table of ContentsPreface
1. Introduction to Probability 1.1. Engineering Applications of Probability 1.2. Random Experiments and Events 1.3. Definitions of Probability 1.4. The RelativeFrequency Approach 1.5. Elementary Set Theory 1.6. The Axiomatic Approach 1.7. Conditional Probability 1.8. Independence 1.9. Combined Experiments 1.10. Bernoulli Trials 1.11. Applications of Bernoulli 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 ProbabilityRevisited 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 of Statistics 4.1. Introduction 4.2. Sampling TheoryThe Sample Mean 4.3. Sampling TheoryThe 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 Process 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 7.2. Relation of Spectral Density to the Fourier Transform 7.3. Properties of Spectral Density 7.4. Spectral Density and the Complex Frequency Plane 7.5. MeanSquare Values From Spectral Density 7.6. Relation of Spectral Density to the Autocorrelation Function 7.7. White Noise 7.8. CrossSpectral Density 7.9. Autocorrelation Function Estimate of Spectral Density 7.10. Periodogram Estimate of Spectral Density 7.11. Examples and Applications of Spectral Density 8. Response of Linear Systems to Random Inputs 8.1. Introduction 8.2. Analysis in the Time Domain 8.3. Mean and MeanSquare Value of System Output 8,4. Autocorrelation Function of System Output 8.5. Crosscorrelation between Input and Output 8.6. Example of TimeDomain System Analysis 8.7. Analysis in the Frequency Domain 8.8. Spectral Density at the System Output 8.9. CrossSpectral Densities between Input and Output 8.10. Examples of FrequencyDomain Analysis 8.11. Numerical Computation of System Output 9. Optimum Linear Systems 9.1. Introduction 9.2. Criteria of Optimality 9.3. Restrictions on the Optimum System 9.4. Optimization by Parameter Adjustment 9.5. Systems That Maximize SignaltoNoise Ratio 9.6. Systems That Minimize MeanSquare Error Appendices A. Mathematical Tables A.1. Trigonometric Identities A.2. Indefinite Integrals A.3. Definite Integrals A.4. Fourier Transform Operations A.5. Fourier Transforms A.6. OneSided Laplace Transforms B. Frequently Encountered Probability Distributions B.1. Discrete Probability Functions B.2. Continuous Distributions C. Binomial Coefficients D. Normal Probability Distribution Function E. The QFunction F. Student's t Distribution Function G. Computer Computations H. Table of Correlation FunctionSpectral Density Pairs I. Contour Integration Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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