A bound on the deviation probability for sums of non-negative random variables.

Abstract

This paper presents a novel power spectrum-based method for fractal analysis of surface electromyography signals. This method, named the bi-phase power spectrum method, provides a bi-phase power-law which represents a multi-scale statistically self-affine signal. This form of statistical self-affinity provides an accurate approximation for stochastic signals originating from a strong non-linear combination of a number of similar distributions, such as surface electromyography signals which are formed by the summation of a number of single muscle fiber action potentials. This power-law is characterized by a set of spectral indicators, which are related to distributional and geometrical characteristics of the electromyography signal's interference pattern. These novel spectral indicators are capable of sensing the effects of motor units' recruitment and shape separately by exploiting the geometry of the interference pattern. The bi-phase power spectrum method is compared to geometrical techniques and the 1/f(alpha) approach for fractal analysis of electromyography signals. The extracted indicators using the bi-phase power spectrum method are evaluated in the context of force and joint angle and the results of a human study are presented. Results demonstrate that the bi-phase power spectrum method provides reliable information, consisting of components capable of sensing force and joint angle effects separately, which could be used as complementary information for confounded conventional measures.