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Probabilistic Methods of Signal and System Analysis (Oxford Series in Electrical and Computer Engineering)

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Publisher 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 Contents

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. 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

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. 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

Index

Product Details

ISBN:
9780195123548
Author:
Cooper, George R.
Author:
McGillem, Clare D.
Author:
null, George R.
Author:
McGillem, The Late Clare D.
Author:
null, the late Clare D.
Publisher:
Oxford University Press, USA
Location:
New York :
Subject:
Engineering - Electrical & Electronic
Subject:
Electronics - General
Subject:
Engineering
Subject:
System analysis
Subject:
Computer Engineering
Subject:
Signal processing
Subject:
Engineering / Electrical
Subject:
Technology | Electrical
Subject:
Electricity
Subject:
Engineering and Technology | Electrical and Computer Engineering
Subject:
Probabilities
Subject:
Signal processing -- Statistical methods.
Subject:
Engineering & Technology | Electrical & Computer Engineering
Subject:
Electricity-General Electricity
Copyright:
Edition Number:
3
Edition Description:
Hardcover
Series:
Oxford Series in Electrical and Computer Engineering
Series Volume:
176
Publication Date:
19980931
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
210 line illus.
Pages:
496
Dimensions:
7.5 x 9.2 x 1.2 in 2.225 lb

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