Segmented fractal dimension measurement of 1-D signals: a wavelet based method
H.B. Nugraha, Armein Z. R. Langi · Asia Pacific Conference on Circuits and Systems · 2003
Fractal dimension is an important characteristic of signals that contain information about their structure complexity. Although, fractal dimension estimation of geometric objects has shown very good results, it is a big problem to estimate the dimension of a 1-D signal. As the dynamics of the signal may vary over time, then its fractal dimension also varies over time. This paper shows our estimations of fractal dimensions of 1-D signal based on wavelet coefficients which are obtained from the maxima lines of a continuous wavelet transform. Instead of their exact estimated values, we are more interested in analyzing their dimension variation over time. Our measurement shows that a stationary signal has relatively constant dimension, on the other hand, a non-stationary signal has varying dimension. These measurements lead us to acquire a different method of signal characterization.