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# Probabilistic Methods of Signal and System Analysis

## byGeorge R. Cooper, the late Clare D. McGillem

### Hardcover | August 1, 1998

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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 andpracticing 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, computercomputation 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 beenadded. A separate appendix discusses and illustrates the application of computers to signal and system analysis.

### Details & Specs

Title:Probabilistic Methods of Signal and System AnalysisFormat:HardcoverDimensions:496 pages, 7.52 × 9.21 × 1.18 inPublished:August 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0195123549

ISBN - 13:9780195123548

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Table of Contents

Preface1. Introduction to Probability1.1. Engineering Applications of Probability1.2. Random Experiments and Events1.3. Definitions of Probability1.4. The Relative-Frequency Approach1.5. Elementary Set Theory1.6. The Axiomatic Approach1.7. Conditional Probability1.8. Independence1.9. Combined Experiments1.10. Bernoulli Trials1.11. Applications of Bernoulli Trials2. Random Variables2.1. Concept of a Random Variable2.2. Distribution Functions2.3. Density Functions2.4. Mean Values and Moments2.5. The Gaussian Random Variable2.6. Density Functions Related to Gaussian2.7. Other Probability Density Functions2.8. Conditional Probability Distribution and Density Functions2.9. Examples and Applications3. Several Random Variables3.1. Two Random Variables3.2. Conditional Probability--Revisited3.3. Statistical Independence3.4. Correlation between Random Variables3.5. Density Function of the Sum of Two Random Variables3.6. Probability Density Function of a Function of Two Random Variables3.7. The Characteristic Function4. Elements of Statistics4.1. Introduction4.2. Sampling Theory--The Sample Mean4.3. Sampling Theory--The Sample Variance4.4. Sampling Distributions and Confidence Intervals4.5. Hypothesis Testing4.6. Curve Fitting and Linear Regression4.7. Correlation Between Two Sets of Data5. Random Processes5.1. Introduction5.2. Continuous and Discrete Random Processes5.3. Deterministic and Nondeterministic Random Processes5.4. Stationary and Nonstationary Random Processes5.5. Ergodic and Nonergodic Random Processes5.6. Measurement of Process Parameters5.7. Smoothing Data with a Moving Window Average6. Correlation Functions6.1. Introduction6.2. Example: Autocorrelation Function of a Binary Process6.3. Properties of Autocorrelation Functions6.4. Measurement of Autocorrelation Functions6.5. Examples of Autocorrelation Functions6.6. Crosscorrelation Functions6.7. Properties of Crosscorrelation Functions6.8. Examples and Applications of Crosscorrelation Functions6.9. Correlation Matrices For Sampled Functions7. Spectral Density7.1. Introduction7.2. Relation of Spectral Density to the Fourier Transform7.3. Properties of Spectral Density7.4. Spectral Density and the Complex Frequency Plane7.5. Mean-Square Values From Spectral Density7.6. Relation of Spectral Density to the Autocorrelation Function7.7. White Noise7.8. Cross-Spectral Density7.9. Autocorrelation Function Estimate of Spectral Density7.10. Periodogram Estimate of Spectral Density7.11. Examples and Applications of Spectral Density8. Response of Linear Systems to Random Inputs8.1. Introduction8.2. Analysis in the Time Domain8.3. Mean and Mean-Square Value of System Output8,4. Autocorrelation Function of System Output8.5. Crosscorrelation between Input and Output8.6. Example of Time-Domain System Analysis8.7. Analysis in the Frequency Domain8.8. Spectral Density at the System Output8.9. Cross-Spectral Densities between Input and Output8.10. Examples of Frequency-Domain Analysis8.11. Numerical Computation of System Output9. Optimum Linear Systems9.1. Introduction9.2. Criteria of Optimality9.3. Restrictions on the Optimum System9.4. Optimization by Parameter Adjustment9.5. Systems That Maximize Signal-to-Noise Ratio9.6. Systems That Minimize Mean-Square ErrorAppendicesA. Mathematical TablesA.1. Trigonometric IdentitiesA.2. Indefinite IntegralsA.3. Definite IntegralsA.4. Fourier Transform OperationsA.5. Fourier TransformsA.6. One-Sided Laplace TransformsB. Frequently Encountered Probability DistributionsB.1. Discrete Probability FunctionsB.2. Continuous DistributionsC. Binomial CoefficientsD. Normal Probability Distribution FunctionE. The Q-FunctionF. Student's t Distribution FunctionG. Computer ComputationsH. Table of Correlation Function--Spectral Density PairsI. Contour IntegrationIndex

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