# Applications of Random Process Excursion Analysis

## 1st Edition

**Authors:**Irina S. Brainina

**eBook ISBN:**9780124104693

**Hardcover ISBN:**9780124095014

**Imprint:**Elsevier

**Published Date:**12th July 2013

**Page Count:**252

## Description

This book addresses one of the key problems in signal processing, the problem of identifying statistical properties of excursions in a random process in order to simplify the theoretical analysis and make it suitable for engineering applications. Precise and approximate formulas are explained, which are relatively simple and can be used for engineering applications such as the design of devices which can overcome the high initial uncertainty of the self-training period.** **The information presented in the monograph can be used to implement adaptive signal processing devices capable of detecting or recognizing the wanted signals (with a priori unknown statistical properties) against the background noise. The applications presented can be used in a wide range of fields including medicine, radiolocation, telecommunications, surface quality control (flaw detection), image recognition, thermal noise analysis for the design of semiconductors, and calculation of excessive load in mechanics.

## Key Features

- Introduces English-speaking students and researchers in to the results obtained in the former Soviet/ Russian academic institutions within last few decades.
- Supplies a range of applications suitable for all levels from undergraduate to professional
- Contains computer simulations

## Readership

Researchers and practitioners working on engineering applications of communications

## Table of Contents

Dedication

Preface

Introduction

1. Probability Characteristics of Random Processes

1.1 A Historical Sketch of Methods Applied for Studying Parameters of Excursions in Broadband Random Processes

1.2 The Use of Excursion Statistics for Practical Purposes

2. Study of Informative Parameters of Excursions in Stationary Random Processes

2.1 Relation Between Two Variances: That of the Number of Level Crossings and That of the Number of Excursions in an Interval of Length

2.2 Distribution of Time to the First Zero Crossing

2.3 Distribution of Time to the First Moment When Zero Level Is Crossed in a Given Direction

3. Estimation of Distribution Densities of Excursion Durations for Random Stationary Broadband Signals

3.1 Estimation of Distribution Density of Zero-Crossing Intervals for Random Processes Symmetrical About Zero

3.2 One Way to Increase the Accuracy of the First Approximation for the Distribution Density of Level-Crossing Time Intervals in a Stationary Random Process

3.3 Methods of Calculating Level-Crossing Parameters for Certain Classes of Non-Gaussian Stationary Random Processes

4. Estimating Certain Informative Parameters of Random Process Excursions Above a Given Level

4.1 Estimating the Variance in Duration of Intervals Between Successive Excursions Above a Given Level in a Stationary Random Process

4.2 Estimating Exponential Tail Parameters for Distribution of Excursions in Stationary Random Processes

4.3 A Study into the Relation Between the Relative Root-Mean-Square Error of Measurement of the Cumulative Distribution Function of a Stationary Random Process and the Observation Time

5. Using a Family of Correlation Functions of a Clipped Random Process to Increase the Accuracy of Level-Crossing Parameters Estimation

5.1 One Method for Calculating Parameters of Zero Crossings in Broadband Centered Random Processes

5.2 One Method for Calculating Parameters of Crossing a Given Standardized Threshold Level by a Random Process

5.3 Estimating the Distribution of Values for the Total Duration of Two or More Successive Excursions of a Random Process Above a Given Threshold

6. Estimates Obtained Through the Study of Certain Less-Known Parameters of Excursions in Differentiable Random Processes

6.1 Distribution Density of Time Before the Next Point Where the Set Upper or Lower Boundary Is Reached by a Differentiable Random Process

6.2 On the Distribution of Random Process Excursion Areas for Excursions Above a Given Level

7. Design Methodology of Adaptable Analyzers Used to Measure the Parameters of Excursions in Stationary Random Processes

7.1 Principal Features of Random Process Parameter Analyzers

7.2 The Analyzer of Duration Values Distribution Density for Above-Threshold Excursions in Random Processes

7.3 Adaptable Analyzer of Interval Length Distribution for Intervals During Which a Random Signal Remains Within or Goes Beyond Given Boundaries

7.4 The Adaptable Random Signal Amplitude Analyzer

7.5 An Adaptable Analyzer of Areas Under Above-Threshold Excursions of Random Processes

7.6 One Way to Measure the Variance in a Broadband Centered Gaussian Random Process

Appendix 1. PC Simulations of Gaussian and Rayleigh Random Processes

Appendix 2. Simulation of the Distribution of Time to the Next Boundary Crossing in Gaussian and Rayleigh Random Processes

Appendix 3. Simulation of Distribution Densities for Areas Enveloped by Above-Threshold or Below-Threshold Excursions of Gaussian and Rayleigh Random Process Curves

References

## Details

- No. of pages:
- 252

- Language:
- English

- Copyright:
- © Elsevier 2013

- Published:
- 12th July 2013

- Imprint:
- Elsevier

- eBook ISBN:
- 9780124104693

- Hardcover ISBN:
- 9780124095014

## About the Author

### Irina S. Brainina

### Affiliations and Expertise

Povolzhye State University of Telecommunications and Informatics (PSUTI), Russia

## Reviews

"...unique in its description of some of the aspects of the theory of excursions for random processes and its applications...equally useful for senior university students as well as for scientists and engineers."--**Zentralblatt MATH, Applications of Random Process Excursion Analysis**

*"…addresses one of the key problems in signal processing, the problem of identifying statistical properties of excursions in a random process in order to simplify the theoretical analysis and make it suitable for engineering applications. Precise and approximate formulas are explained, which are relatively simple and can be used for engineering applications such as the design of devices which can overcome the high initial uncertainty of the self-training period."--**zbMATH.org,* June 19, 2014*"Brainina shares the results of her many years studying the theory of excursions as it applies to adaptive radio communications systems. A highlight is that she manages to apply calculation methods chosen for Gaussian processes to a larger class of non-Gaussian random processes."--**Reference & Research Book News,* October 2013