Adaptive Filters Using Fractal Dimension of Data

By Fred J. Harris & Deborah S. Kin

Abstract:

The fractal dimension of a data series can be used as a sensitive indicator of the temporal variability of a signal. Smooth continuous signals have fractal dimension of one while signals with discontinuities and very noisy signals have fractal dimension between one and two. This measure, estimated over short sliding intervals, can be used to adjust the local spectral characteristics of a digital filter to emphasize or to suppress local temporal features of the signal. We have examined and have compared the performance of a number of filters with parameters controlled by the short term fractal dimension of two classes of signals. The processed signals were sinusoids and square waves with varying amounts of additive white Gaussian noise. The filter structures included the finite impulse response (FIR), infinite impulse response (IIR), and edian filters. We examined two methods of changing the filters with fractal dimension; these were, changing between fixed filters as the fractal dimension crossed thresholds, and changing filter parameters proportionally with the fractal dimension. In addition to describing the filtering process we also report on methods for estimating the fractal dimension over the sliding Interval.

Download Document
(This item is protected by original copyright)

Rate this document: