Mean level signal crossing rate for an arbitrary stochastic process

Harold T. Yura, Steen Grüner Hanson

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Abstract

The issue of the mean signal level crossing rate for various probability density functions with primary relevance for optics is discussed based on a new analytical method. This method relies on a unique transformation that transforms the probability distribution under investigation into a normal probability distribution, for which the distribution of mean level crossings is known. In general, the analytical results for the mean level crossing rate are supported and confirmed by numerical simulations. In particular, we illustrate the present method by presenting analytic expressions for the mean level crossing rate for various probability distributions, including ones that previously were unavailable, such as the uniform, the so-called gamma-gamma, and the Rice–Nakagami distribution. However, in a limited number of cases the present results differ somewhat from the result reported in the literature. At present, this discrepancy remains unexplained and is laid open for future discussion.
Original languageEnglish
JournalOptical Society of America. Journal A: Optics, Image Science, and Vision
Volume27
Issue number4
Pages (from-to)797-807
ISSN1084-7529
DOIs
Publication statusPublished - 2010

Bibliographical note

This paper was published in Optical Society of America. Journal A and is made available as an electronic reprint with the permission of OSA. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Cite this

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title = "Mean level signal crossing rate for an arbitrary stochastic process",
abstract = "The issue of the mean signal level crossing rate for various probability density functions with primary relevance for optics is discussed based on a new analytical method. This method relies on a unique transformation that transforms the probability distribution under investigation into a normal probability distribution, for which the distribution of mean level crossings is known. In general, the analytical results for the mean level crossing rate are supported and confirmed by numerical simulations. In particular, we illustrate the present method by presenting analytic expressions for the mean level crossing rate for various probability distributions, including ones that previously were unavailable, such as the uniform, the so-called gamma-gamma, and the Rice–Nakagami distribution. However, in a limited number of cases the present results differ somewhat from the result reported in the literature. At present, this discrepancy remains unexplained and is laid open for future discussion.",
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Mean level signal crossing rate for an arbitrary stochastic process. / Yura, Harold T.; Hanson, Steen Grüner.

In: Optical Society of America. Journal A: Optics, Image Science, and Vision, Vol. 27, No. 4, 2010, p. 797-807.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Mean level signal crossing rate for an arbitrary stochastic process

AU - Yura, Harold T.

AU - Hanson, Steen Grüner

N1 - This paper was published in Optical Society of America. Journal A and is made available as an electronic reprint with the permission of OSA. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

PY - 2010

Y1 - 2010

N2 - The issue of the mean signal level crossing rate for various probability density functions with primary relevance for optics is discussed based on a new analytical method. This method relies on a unique transformation that transforms the probability distribution under investigation into a normal probability distribution, for which the distribution of mean level crossings is known. In general, the analytical results for the mean level crossing rate are supported and confirmed by numerical simulations. In particular, we illustrate the present method by presenting analytic expressions for the mean level crossing rate for various probability distributions, including ones that previously were unavailable, such as the uniform, the so-called gamma-gamma, and the Rice–Nakagami distribution. However, in a limited number of cases the present results differ somewhat from the result reported in the literature. At present, this discrepancy remains unexplained and is laid open for future discussion.

AB - The issue of the mean signal level crossing rate for various probability density functions with primary relevance for optics is discussed based on a new analytical method. This method relies on a unique transformation that transforms the probability distribution under investigation into a normal probability distribution, for which the distribution of mean level crossings is known. In general, the analytical results for the mean level crossing rate are supported and confirmed by numerical simulations. In particular, we illustrate the present method by presenting analytic expressions for the mean level crossing rate for various probability distributions, including ones that previously were unavailable, such as the uniform, the so-called gamma-gamma, and the Rice–Nakagami distribution. However, in a limited number of cases the present results differ somewhat from the result reported in the literature. At present, this discrepancy remains unexplained and is laid open for future discussion.

U2 - 10.1364/JOSAA.27.000797

DO - 10.1364/JOSAA.27.000797

M3 - Journal article

VL - 27

SP - 797

EP - 807

JO - Optical Society of America. Journal A: Optics, Image Science, and Vision

JF - Optical Society of America. Journal A: Optics, Image Science, and Vision

SN - 1084-7529

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ER -