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Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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TL;DR: In this article, the mean length of runs of wave heights and the mean number of waves between the exceedance of a certain level by a group of waves and the next exceedances of the same level by the succeeding groups of waves have been investigated for data from the March 1968 North Atlantic storm.
Abstract: The mean length of runs of wave heights and the mean number of waves between the exceedance of a certain level by a group of waves and the next exceedance of the same level by the succeeding group of waves have been investigated for data from the March 1968 North Atlantic storm. These quantities are compared with corresponding results obtained from the numerical simulation of waves in a computer for both wide and narrow band spectra.
11 citations
TL;DR: In this paper, the effect of high-frequency components in the power spectral density (PSD) of the loading process on the fatigue life of welded steel specimens has been investigated.
11 citations
TL;DR: In this article, the expected number of crossings of a level by a real valued symmetric harmonizable p-stable process defined on the interval [0, T] is given.
11 citations
TL;DR: In this paper, the intersection points of a fixed planar curve with the nodal set of a translationally invariant and isotropic Gaussian random field were studied and the zeros of its normal derivative across the curve.
Abstract: We study the intersection points of a fixed planar curve Γ with the nodal set of a translationally invariant and isotropic Gaussian random field Ψ(r) and the zeros of its normal derivative across the curve. The intersection points form a discrete random process which is the object of this study. The field probability distribution function is completely specified by the correlation G(|r − r'|) = Ψ(r)Ψ(r'). Given an arbitrary G(|r − r'|), we compute the two-point correlation function of the point process on the line, and derive other statistical measures (repulsion, rigidity) which characterize the short- and long-range correlations of the intersection points. We use these statistical measures to quantitatively characterize the complex patterns displayed by various kinds of nodal networks. We apply these statistics in particular to nodal patterns of random waves and of eigenfunctions of chaotic billiards. Of special interest is the observation that for monochromatic random waves, the number variance of the intersections with long straight segments grows like Lln L, as opposed to the linear growth predicted by the percolation model, which was successfully used to predict other long-range nodal properties of that field.
11 citations
Cites methods from "Mathematical Analysis of Random Noi..."
...An exact formula for computing zeros correlations from one dimensional amplitude correlations was derived by Rice in his analysis of random noise [16],[17]....
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TL;DR: In this paper, a non-linear estimator for the ergodic Gauss-Markov process with mean zero and covariance function e −|τ| was proposed.
11 citations