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

To remove small-scale variance and noise, time series of data are generally filtered using a moving window with a specified distribution of weights. Such filters unfortunately smooth sharp changes associated with larger-scale structures. In this study, an adaptive low-pass filter is developed that not only effectively removes random small-scale variations but also retains sudden changes or sharp edges that are part of the large-scale features. These sudden changes include fronts, abrupt shifts in climate, sharp changes associated with a heterogeneous surface, or any jump in conditions associated with change on a larger scale. To construct the filter, gradients on different scales and at different positions in the time series are computed using a multiresolution representation of the data. The low-pass filter adapts to include smaller-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 weights at locations in the original time series where the signal is rapidly varying. As application examples, the filter is applied to turbulence data observed under strong wind conditions and climate data corresponding to 52 years of a Southern Oscillation index.