A time-frequency application with the Stokes-Woodward technique

Elfouhaily et al. (2003) generalized Woodwardʹs 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. An application to water surface waves is given as an example.