Figure 1.
Fractional Gaussian noise and fractional Brownian motion.
Representation of the continuum of fractal processes, with: the two families of fractional Gaussian noise and fractional Brownian motion, the typical correlation and diffusion properties characterizing the two types of processes, and the associated H exponents.
Figure 2.
Graphical signatures of cross-over.
Schematic representation of the typical log-log diffusion plots resulting from SDA and DFA. This figure illustrates how the cross-over phenomenon can be detected using diffusion analysis.
Figure 3.
Mean graphical results for experimental series.
Average log-log diffusion plots obtained from SDA and DFA, and log-log power spectra on the COP position and velocity data (ML axis) collected during quiet standing. The dashed lines in the upper (SDA) and middle graphs (DFA) represent the boundary slopes between persistent and anti-persistent correlation (slope = 1.0 for SDA, and 0.5 for DFA, see text for details). The SDA shows a cross-over phenomenon when applied to position series while both the DFA and PSD analyses show a cross-over in velocity series.
Figure 4.
Representative examples of empirical series of COP position (top) and velocity (bottom).
Series from participant #10, ML axis.
Figure 5.
Representative examples of simulated series of COP position (top) and velocity (bottom).
Figure 6.
Mean graphical results for simulated series.
Average log-log diffusion plots and power spectra obtained from DFA and PSD with simulated position and velocity series. These graphs are based on point-by-point averaging of the results obtained from 26 randomly selected simulated series. The dashed line in the upper plots (DFA) represents the slope of 0.5, corresponding to the boundary between persistent and anti-persistent correlation.
Figure 7.
Effects of age and vision on the average absolute maximal velocity of the COP.
Results are given for the AP axis.
Table 1.
Results of time series analyses for COP position and velocity series.