An Adaptive Multiresolution Data Filter: Applications to Turbulence and Climatic Time Series

Abstract

Abstract 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 appl...