Gaussian Filters for Determining Group Velocities

The problem of filtering dispersed wavetrains by Gaussian filters has been examined. Asymptotic expressions for small bandwidths are obtained for the centroid and for the variance of the filtered signal about its centroid. The forms of the expressions suggest the use of an extrapolation algorithm to estimate the group arrival time. An optimal filter is introduced to aid in selecting a set of corresponding pairs of centroid and bandwidth values for use in the algorithm. For a finite time series, only those pairs whose variances are well within the length of the time series are considered. In this way, the estimated group arrival times are consistent with the information content of the data and are independent of the data extension technique. The method is applied to both synthesized and real signals. The corresponding errors in the group velocity are less than 0.1 and 2 per cent, respectively.