A Comparison of waveform fractal dimension algorithms

The fractal dimension of a waveform represents a powerful tool for transient detection. In particular, in analysis of electroencephalograms and electrocardiograms, this feature has been used to identify and distinguish specific states of physiologic function. A variety of algorithms are available for the computation of fractal dimension. In this study, the most common methods of estimating the fractal dimension of biomédical signals directly in the time domain (considering the time series as a geometric object) are analyzed and compared. The analysis is performed over both synthetic data and intracranial electroencephalogram data recorded during presurgical evaluation of individuals with epileptic seizures. The advantages and drawbacks of each technique are highlighted. The effects of window size, number of overlapping points, and signal-to-noise ratio are evaluated for each method. This study demonstrates that a careful selection of fractal dimension algorithm is required for specific applications.