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 result, 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 vary over time. This paper shows our estimations of fractal dimensions of 1-D signal based on wavelet coefficients which are obtain from maxima lines of continues wavelet transform. Instead of their exact estimated values, we more interested to analyze their dimension variation over time. Our measurement shows that stationer signal has relatively constant dimension, at the other way, non-stationer signal has varying dimension. These measurements lead us to have a different method of signal characterization.