Segmented fractal dimension measurement of 1-D signals: a wavelet based method

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.