Comparison of fractal dimension algorithms using synthetic and experimental data

The fractal dimension (FD) of a waveform represents a powerful tool for transient detection. In particular, in analysis of electroencephalograms (EEG) and electrocardiograms (ECG), this feature has been used to identify and distinguish specific states of physiologic function. A variety of algorithms are available for the computation of FD. In this study, the most common methods of estimating the FD of biomedical signals are analyzed and compared. The analysis is performed over both synthetic data and intracranial EEG (IEEG) data recorded during pre-surgical 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 (SNR) are evaluated for each method. This study demonstrates that a careful selection of FD algorithm is required for specific applications.