Applications of Random Process Excursion Analysis


  • Irina S. Brainina, Povolzhye State University of Telecommunications and Informatics (PSUTI), Russia

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.
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Researchers and practitioners working on engineering applications of communications


Book information

  • Published: July 2013
  • Imprint: ELSEVIER
  • ISBN: 978-0-12-409501-4


"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

Table of Contents



Chapter 1 Probability characteristics of random process excursions

1.1 Methods to determine parameters of excursions for random broadband signals. A historical survey

1.2 Some practical applications of excursion characteristics

Chapter 2 Study of integral parameters of excursions

2.1 Relation between two variances: the variance in the number of level crossings and the variance in the number of excursions within an interval of length

2.2 Cumulative distribution function of time to the next moment when zero level is reached

2.3 Cumulative distribution function of time to the next moment when zero level is crossed in a given direction

Chapter 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 differentiable random process

3.3 Methods of calculating level-crossing parameters for certain classes of non-Gaussian stationary random processes

Chapter 4 Estimating certain informative parameters of random process excursions above a given level

4.1 Estimating the variance in duration of intervals between successive random process excursions above a given standardized level

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 for the cumulative distribution function of a stationary random process and the duration of the part analyzed

Chapter 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

Chapter 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 Estimating areas of shapes formed by a random process curve and a given horizontal line it crosses

Chapter 7 Design methodology of adaptable analyzers used to measure characteristics of excursions in stationary random processes

7.1 Principal features of random process parameter analyzers

7.2 A distribution density analyzer for above-threshold excursion durations in random processes

7.3 An adaptable analyzer of interval length distribution for intervals during which a random signal remains within or goes beyond given boundaries

7.4 An 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 Some data obtained through computer simulations of excursion parameters for broadband Gaussian and Rayleigh random processes

Appendix 2 Simulating the distribution of time before the next point when a Gaussian or Rayleigh random process crosses the given lower or upper boundary

Appendix 3 Simulating the distribution of areas of shapes formed by the curve representing a Gaussian or Rayleigh random process and the given horizontal line

Appendix 4 The set of computer applications for simulating parameters of excursions for broadband Gaussian and Rayleigh random processes (on companion website)