Fractal Dimension Estimation Via Spectral Distribution Function and Its Application to Physiological Signals

Rhythmic signals from physiological systems usually have memory and long-term correlation. They can be modeled as fractional Brownian motion or fractional Gaussian noise depending on if the signals are derived from cumulative effects of nerves and muscles. That is, they can be treated as signals with fractional dimension, and the value of its fractal dimension can be used to characterize the intensity of physiological signals. In this communication, a novel method of dimension estimation based on the calculation of spectral distribution function of discrete-time fractional Gaussian noise using Legendre polynomials as basis set is proposed. The effectiveness of this proposed method is demonstrated in the dynamic behavior of detrusor of the bladder and external urethral sphincter during micturition.