A time-Frequency Application with the Stokes-Woodward technique

Tanos Elfouhaily (1) , Stephan Guignard (2) , Hubert Branger (1) , Donald R. Thompson (3) , Bertrand Chapron (4) , Doug Vandemark (3)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 IUSTI - Institut universitaire des systèmes thermiques industriels
3 APL - Johns Hopkins University Applied Physics Laboratory [Laurel, MD]
4 IFREMER - Institut Français de Recherche pour l'Exploitation de la Mer

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 timefrequency domain. A comparison between a wavelet transform and our time-frequency technique shows good agreement along with new insight into the time occurrence of the nonlinearities or mode coupling. Application to water surface waves is given in this letter as an example.

Mots clés: AM-FM modulations; mode coupling; instantaneous frequency; instantaneous amplitude; horizontal asymmetry; vertical asymmetry; wave-wave interaction; wind-waves; nonlinear hydrodynamic processes; time-frequency distributions

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Analyse de données, Statistiques et Probabilités [physics.data-an]; Physique mathématique [math-ph]; Océan, Atmosphère

Tanos Elfouhaily, Stephan Guignard, Hubert Branger, Donald R. Thompson, Bertrand Chapron, et al.. A time-Frequency Application with the Stokes-Woodward technique. IEEE Transactions on Geoscience and Remote Sensing, 2003, 41, n° 11 part. 2, pp.2670- 2673. ⟨10.1109/TGRS.2003.817202⟩. ⟨hal-00014605⟩