In this paper we investigate the feasibility of using time frequency distributions to measure time-localized phase and group velocities given wave elevation time series measured at two points spatially separated in the direction of wave propagation. The results are compared to those obtained experimentally from classical Fourier based cross-power spectra, which of course provide no time localization, and to theoretical estimates of phase and group velocity.
Classical Fourier-based cross-power spectra analysis (Beall et.al, 1988) has been successfully utilized to estimate dispersion relations, and phase and group velocities. The general approach is to monitor the wave field in the direction of propagation with two probes spaced a fraction of a wavelength apart. The phase of the cross-power spectrum measures the phase shift (i.e., the phase difference) that each spectral component undergoes in traveling from the first to the second probe. Since this phase shift is equal to product of the wave number times the distance of separation, the wave number as a function of frequency can be estimated by dividing the phase shift by the distance of separation. Of course the Fourier approach does not provide any time localization and, furthermore, requires moderately long data lengths. On the other hand, time-frequency distributions provide simultaneous time and frequency information, in that they indicate how the "power" of a signal is distributed over time and frequency. This raises the question (which is also the objective of this paper) as to whether such distributions might be able to provide time-localized measurements of phase and group velocity, given the same type of two wave time series used in the Fourier approach. Unfortunately, the common class of timefrequency distributions known as Cohen's class apply to only a single time series (not two) and, furthermore, no phase information
