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Relationship Between Self-Similarity and Auto-Correlation Functions

The self-similarity parameter of an integrated time series is related to the more familiar auto-correlation function, tex2html_wrap_inline1157, of the original (non-integrated) signal. Briefly:

The tex2html_wrap_inline1001 exponent can also be viewed as an indicator of the ``roughness'' of the original time series: the larger the value of tex2html_wrap_inline1001, the smoother the time series. In this context, 1/f noise can be interpreted as a compromise or ``trade-off'' between the complete unpredictability of white noise (very rough ``landscape'') and the much smoother landscape of Brownian noise [18].

In the next sections, we apply these scaling analyses to the output of two complex integrated neural control systems, namely those regulating human heart rate and gait dynamics in health and disease.


next up previous
Next: Fractal Dynamics of Human Up: Fractal Analysis Methods Previous: Detrended Fluctuation Analysis (DFA)