DISCRETE WAVELET IMPLEMENTATION OF THE MULTIFRACTAL ANALYSIS OF SINGULAR SIGNALS

Abstract

The discrete wavelet analysis has been used in implementing the multifractal formalism on singular signals. We show that the discrete wavelet transform, so called the multiresolution analysis, can determine the singularity spectrum of multifractal measures directly from the scaling behavior of the partition function, and account for the multifractal nature of the time series obtained from chaotic phenomena. As an example, we discuss the applications of our wavelet analysis to the fractal measures from the two scale Canter set and the time series from the critical circle map.