Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T20:14:09.366Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave-length and amplitude in Gaussian noise

Published online by Cambridge University Press:  01 July 2016

Georg Lindgren
Georg Lindgren*
Affiliation:
University of Lund, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

We give moment approximations to the density function of the wavelength, i. e., the time between “a randomly chosen” local maximum with height u and the following minimum in a stationary Gaussian process with a given covariance function. For certain processes we give similar approximations to the distribution of the amplitude, i. e., the vertical distance between the maximum and the minimum. Numerical examples and diagrams illustrate the results.

Keywords

CROSSING PROBLEMSLOCAL MAXIMAMOMENT RELATIONSSAMPLE FUNCTION PROPERTIESAMPLITUDE IN GAUSSIAN NOISEAMPLITUDE IN STATIONARY PROCESSESWAVE LENGTH IN GAUSSIAN NOISEWAVE LENGTH IN STATIONARY PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 4 , Issue 1 , April 1972 , pp. 81 - 108
Copyright
Copyright © Applied Probability Trust 1972 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Belyaev, Yu. K. (1966) On the number of intersections of a level by a Gaussian stochastic process. Teor. Veroyat. Primen. 11, 120–128.Google Scholar
[2] Cartwright, D. E. and Longuet-Higgins, M. S. (1956) The statistical distribution of the maxima of a random function. Proc. Roy. Soc. London A, 237, 212–232.Google Scholar
[3] Cramér, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
[4] Cramér, H., Leadbetter, M. R. and Serfling, R. J. (1971) On distribution function - moment relationships in a stationary point process. Z. Wahrscheinlichkeitsth. 18, 1–8.CrossRefGoogle Scholar
[5] Kac, M. and Slepian, D. (1959) Large excursions of Gaussian processes. Ann, Math. Statist. 30, 1215–1228.CrossRefGoogle Scholar
[6] Leadbetter, M. R. (1969) On the distribution of the time between events in a stationary stream of events. J. R. Statist. Soc. B 31, 295–302.Google Scholar
[7] Lindgren, G., (1970) Some properties of a normal process near a local maximum. Ann. Math. Statist. 41, 1870–1883.Google Scholar
[8] Longuet-Higgins, M. S. (1962) The distribution of intervals between zeros of a stationary random function. Phil. Trans. Roy. Soc. London A, 254, 557–599.Google Scholar
[9] Rice, S. O. (1945) Mathematical analysis of random noise. Bell Syst. Tech. J. 24, 46–156.Google Scholar
[10] Rice, S. O. (1958) Distribution of the duration of fades in radio transmission Gaussian noise model. Bell Syst. Tech. J. 37, 581–635.CrossRefGoogle Scholar
[11] Sjöström, S. (1961) On random load analysis. Trans. Roy. Inst. of Tech. Stockholm 181, 1–41.Google Scholar
[12] Slepian, D. (1961) First passage time for a particular Gaussian process. Ann. Math. Statist. 32, 610–612.Google Scholar
[13] Wong, E. (1966) Some results concerning zero-crossings in Gaussian noise. SIAM J. Appl. Math. 14, 1246–1254.Google Scholar