Performance study of fractal dimensionʹs estimated algorithms of Time series Waveforms

The fractal dimension of a waveform represents a powerful tool for transient detection in signals. In particular, in analysis of electroencephalograms (EEG) and electrocardiograms (ECG), this feature has used to identify and distinguish specific states of physiologic function. There are many notions of fractal dimension, and various algorithms have proposed for computing them. In this paper, we study performance of Katz, Sevcik, Higuchi and MRBC methods of computing fractal dimension of waveforms. In order to evaluate the performance of these methods, we use three kind of signals, namely, Fractional Brownian motion, Weierstrass cosine function and Weierstrass-Mandelbrot cosine function. The number of data samples is equal to 100, 250, 500, 1000 and 2000. The time duration of every algorithms calculated until the shortest way for estimation algorithm to realize. The results show that the highest accuracy in the estimation of the fractal dimension is belong to Higuchi method and when the number of data vary, its performance is the same. However, this method due to the nature of algorithms requires more time for implementation and in all methods by increasing of the number of data, duration time for calculation increases. Katz algorithm is the fastest method, but using of this method not recommended due to lack of sufficiently accurate.