# Random Signal Analysis in Engineering Systems

## 1st Edition

Authors:
eBook ISBN: 9780323156271
Imprint: Academic Press
Published Date: 28th September 1987
Page Count: 316
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## Description

Random Signal Analysis in Engineering Systems covers the concepts of probability, random variables, averages, simulation, and random signals. The book discusses set theory and probability; random variables and vectors; and the functions of random variables. The text also describes the statistical averages; simulation; statistical inference; and random processes. Undergraduate engineering students will find the book useful.

## Table of Contents

Preface

1 Set Theory and Probability

1.1 Introduction

1.2 Set Theory

1.3 Probability Theory

1.4 Conditional Probability and Statistical Independence

Problems

2 Random Variables and Vectors

2.1 Random Variables

2.2 Gaussian Random Variable

2.3 Other Random Variables

2.4 Random Vectors

2.5 Conditional Distribution and Density Functions

Problems

3 Functions of Random Variables

3.1 One-to-One Transformation of Random Variables

3.2 One-to-One Transformation of Random Vectors

3.3 Non-One-to-One Transformation

3.4 Sum of Random Variables

3.5 Special Transformations

Problems

4 Statistical Averages

4.1 Expected Value

4.2 Characteristic Function

4.3 Multiple Random Variables

4.4 TV-Dimensional Gaussian

4.5 Binary Communication Scheme

4.6 Inequalities

4.7 Central Limit Theorem

Problems

5 Simulation

5.1 Theoretical Histogram

5.2 Pseudorandom Numbers

5.3 Empirical Histogram

5.4 Goodness of Fit

5.5 Simulation Confidence Statements

5.6 Correlated Random Variables

Problems

6 Statistical Inference

6.1 Sampling and Estimation

6.2 Maximum Likelihood Estimation

6.3 Sequential Estimation

6.4 Random Parameter Estimation

Problems

7 Random Processes

7.1 Statistical Description

7.2 Statistical Averages

7.3 Spectral Density

7.4 Linear Systems with Random Inputs

Problems

Appendix A: Evaluation of Gaussian Probabilities

A.l Q Function Evaluation

A.2 Inverse Q Function

Appendix B: Sum of N Uniform Random Variables

Appendix C: Moments of Random Variables

Appendix D: Matrix Notation

Appendix E: Mathematical Quantities

E.l Trigonometric Identities

E.2 Indefinte Integrals

E.3 Definite Integrals

E.4 Series

E.5 Fourier Transforms

Bibliography

Answers to Selected Problems

Index

## Details

No. of pages:
316
Language:
English
Copyright:
© Academic Press 1987
Published:
Imprint:
Academic Press
eBook ISBN:
9780323156271