Probability distribution applicable to non-Gaussian random processes

Ochi, Michel K.; Ahn, Kyungmo

doi:10.1016/0266-8920(94)90017-5

Cited by 45 publications

(10 citation statements)

References 10 publications

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“…This energy augmentation, therefore, provides the difference between the bare and the dressed spectra as originally introduced and discussed in [6]. The difference between bare and dressed spectra as given in (8) can also be assimilated with the bicoherence function of phase coupling as introduced by [7] and utilized by [8]. Indeed, energy of phase coupling to second order is another manifestation of the bispectrum defined as the Fourier transform of the skewness function using a third order cumulant.…”

Section: B Temporal and Statistical Modulationmentioning

confidence: 96%

“…being the number of points of the series in and we have (9) Discretized pdfs are obtained this way. We associate this excess spectrum in (8) with terms added to the bare spectrum as contributing to the energy increase at higher frequencies due to the nonlinearities or mode coupling. This energy augmentation, therefore, provides the difference between the bare and the dressed spectra as originally introduced and discussed in [6].…”

Section: B Temporal and Statistical Modulationmentioning

confidence: 99%

“…The 2-D probability density distributions in (2) and in (8) are different and are to be estimated from the time series itself if they are not known a priori. The surface elevation time series provides, thanks to the zero-crossing technique, time series of , , and the instantaneous frequency.…”

Section: B Temporal and Statistical Modulationmentioning

confidence: 99%

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A time-frequency application with the stokes-woodward technique

Elfouhaily

Guignard

Branger

et al. 2003

IEEE Trans. Geosci. Remote Sensing

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In a recent paper, we have generalized Woodward's theorem and applied it to the case of random signals jointly modulated in amplitude and frequency. This generalization yields a new spectral technique to estimate the amount of energy due to mode coupling without calling for higher order statistics. Two power spectra are detected; the first is related to the independent modes, and the second contains extra energy caused by mode coupling. This detection is now extended from frequency to time-frequency domain. A comparison between a wavelet transform and our timefrequency technique shows good agreement along with new insight into the time occurrence of the nonlinearities or mode coupling. An application to water surface waves is given in this letter as an example.

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Section: B Temporal and Statistical Modulationmentioning

confidence: 96%

Section: B Temporal and Statistical Modulationmentioning

confidence: 99%

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A time-frequency application with the stokes-woodward technique

Elfouhaily

Guignard

Branger

et al. 2003

IEEE Trans. Geosci. Remote Sensing

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show abstract

“…This energy augmentation therefore provides the difference between the bare and the dressed spectra as discussed in [Elfouhaily et al, 1999]. The difference can also be assimilated with the bicoherence function of phase coupling as introduced by Kim and Powers [1979] and utilized by Ochi and Ahn [1994]. Indeed, energy of phase coupling to second order is another manifestation of the bispectrum defined as the Fourier transform of the skewness function using a third order cumulant.…”

Section: Temporal and Statistical Modulationmentioning

confidence: 99%

Analysis of random nonlinear water waves: the Stokes–Woodward technique

Elfouhaily

Joelson

Guignard

et al. 2003

Comptes Rendus. Mécanique

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A generalization of the Woodward's theorem is applied to the case of random signals jointly modulated in amplitude and frequency. This yields the signal spectrum and a rather robust estimate of the bispectrum. Furthermore, higher order statistics that quantify the amount of energy in the signal due to nonlinearities, e.g., wave-wave interaction in the case of water waves, can be inferred. Considering laboratory wind generated water waves, comparisons between the presented generalization and more standard techniques allow to extract the spectral energy due to nonlinear wave-wave interactions. It is shown that our analysis extends the domain of standard spectral estimation techniques from narrow-band to broad-band processes.

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“…Different strategies to choose the function g have been proposed and studied in [8][9][10] and [11]. An advantage with the transformed Gaussian models is that they are easy to simulate from and that the fatigue damage can be related to Gaussian loads where a lot of results are known.…”

Section: Introductionmentioning

confidence: 99%