AN ADAPTIVE MULTIRESOLUTION DATA FILTER - APPLICATIONS TO TURBULENCE AND CLIMATIC TIME-SERIES

To remove small-scale variance and noise, time series of data are gene rally filtered using a moving window with a specified distribution of weights. Such filters unfortunately smooth sharp changes associated wi th larger-scale structures. In this study, an adaptive low-pass filter is developed that not only effectively removes random small-scale var iations but also retains sudden changes or sharp edges that are part o f the large-scale features. These sudden changes include fronts, abrup t shifts in climate, sharp changes associated with a heterogeneous sur face, or any jump in conditions associated with change on a larger sca le. To construct the filter, gradients on different scales and at diff erent positions in the time series are computed using a multiresolutio n representation of the data. The low-pass filter adapts to include sm aller-scale variations at positions in the time series where the small -scale gradient is steep and represents change on a larger scale. The action of the filter is to apply a more concentrated distribution of w eights at locations in the original time series where the signal is ra pidly varying. As application examples, the filter is applied to turbu lence data observed under strong wind conditions and climate data corr esponding to 52 years of a Southern Oscillation index.