A time-scale representation of EEG Higuchi fractal dimension

Higuchi Fractal Dimension (HFD) is a widely used nonlinear metric with extensive application in biological signal analysis, including electroencephalography (EEG) signal processing. HFD relies on a single free parameter, k_max, which is the maximum scale in samples, used to assess the signal's self-similarity. While fractal dimension estimation is independent of sampling frequency (Fs) in ideally fractal signals, EEG signals do not exhibit ideal fractality, also making the HFD estimates sensitive to both parameter k_max and sampling frequency. As a result, HFD results reported across studies are difficult to compare with different parameter settings. In this work, we emphasize the need to account for the sampling frequency and present the HFD results in terms of the maximum time interval, t_max = k_max/Fs, rather than k_max, thereby facilitating comparisons across studies. Additionally, we demonstrate that the choice of maximum time interval (t_max) determines the frequency range that HFD focuses on, improving the interpretation of the results and enabling a more informed parameter selection.