Probabilistic Methods of Signal and System Analysis / Edition 3

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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 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.

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Product Details

Meet the Author

both of Purdue University
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Table of Contents

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. 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 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 of 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 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. 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. 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 Mean-Square Value of System Output
8,4. Autocorrelation Function of System Output
8.5. Crosscorrelation between Input and Output
8.6. Example of Time-Domain System 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 Optimality
9.3. Restrictions on the Optimum System
9.4. Optimization by Parameter Adjustment
9.5. Systems That Maximize Signal-to-Noise Ratio
9.6. Systems That Minimize Mean-Square Error
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. One-Sided 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 Q-Function
F. Student's t Distribution Function
G. Computer Computations
H. Table of Correlation Function—Spectral Density Pairs
I. Contour Integration

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Sort by: Showing all of 4 Customer Reviews
  • Anonymous

    Posted January 6, 2008

    Excellent introductory textbook

    This textbook presents the theory very simply and clearly and includes drill exercises with answers so that you can check your understanding. However, the lack of answers to selected problems can make the text difficult to use for self study.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted March 25, 2001

    Will one be lost, thirty or Frustrated? Probably.

    Beautiful cover. Simple, yet entirely descriptive of the material. The teaching method of this textbook, however, could very significantly be improved. Because of the lack of examples, for example in the second chapter that deals with random variables, understanding the concept was a bit overwhelming. This lack of examples left one a bit 'thirsty', if you will. The authors explain that these answers are not listed in the same sequence as the questions because they wanted to provide the student with 'an additional challenge.' So, if one wanted a sip of fullfilment by trying the exercises, one became even more frustrated, perturbed and discouraged. Also, the chapter problems are not divided in order of the sub chapters, so one's left even more lost. I would have been greatly grateful if a study aid with solutions had been made available and if the exercises' answers were in the correct ordering of the questions. I also would have gotten more out of my learning experince if examples that related to the chapter problems had been added.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted July 18, 2003

    Would NOT use again

    I used this book at UC Denver. Terrible. Text has some errors, extremely few examples. Students have complained about this text for several semesters.

    0 out of 1 people found this review helpful.

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  • Anonymous

    Posted May 29, 2001


    This is a horrible textbook. There are basically no examples at all, and no problems that are worked out at length. If you are lost on a particular topic, this book cannot help you AT ALL. If you have a professor who is not a very good teacher, this book leaves you nothing to fall back on. I could have gone the whole semester without even buying this book. What a total waste of money!

    0 out of 1 people found this review helpful.

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