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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 2 — Feb. 1, 2012
  • pp: 164–166

Mean level signal crossing rate for an arbitrary stochastic process: comment

José Cândido S. Santos Filho, Michel D. Yacoub, and George K. Karagiannidis  »View Author Affiliations


JOSA A, Vol. 29, Issue 2, pp. 164-166 (2012)
http://dx.doi.org/10.1364/JOSAA.29.000164


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Abstract

In J. Opt. Soc. Am. A 27, 797 (2010), Yura and Hanson derived what they claim to be “a general expression for the mean level crossing rate for an arbitrary” random process following any desired probability distribution function. On the other hand, the authors themselves assert that in some cases their results “differ somewhat from the result reported in the literature.” This discrepancy “remains unexplained” by the authors “and is laid open for future discussion.” In this note, we explain the reason for such discrepancy and show that the Yura-Hanson formula is indeed a special-case solution. A more general solution is then given that is applicable to arbitrary random processes and that is fully consistent with the Rice mean level crossing rate formula.

© 2012 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.1670) Coherence and statistical optics : Coherent optical effects
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: September 27, 2011
Manuscript Accepted: October 27, 2011
Published: January 9, 2012

Citation
José Cândido S. Santos Filho, Michel D. Yacoub, and George K. Karagiannidis, "Mean level signal crossing rate for an arbitrary stochastic process: comment," J. Opt. Soc. Am. A 29, 164-166 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-2-164


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References

  1. H. T. Yura and S. G. Hanson, “Mean level signal crossing rate for an arbitrary stochastic process,” J. Opt. Soc. Am. A 27, 797–807 (2010). [CrossRef]
  2. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. (McGraw-Hill, 2002).
  3. S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).
  4. J. C. S. Santos Filho and M. D. Yacoub, “On the second-order statistics of Nakagami fading simulators,” IEEE Trans. Commun. 57, 3543–3546 (2009). [CrossRef]

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