Parametric estimation of the continuous non-stationary spectrum and its dynamics in surface EMG studies

Abstract

Frequency spectrum of surface electromyographic signals (SEMGs) exhibit a non-stationary nature even in the case of constant level isometric muscle contractions due to changes related to muscle fatigue processes. These changes can be evaluated by methods for estimation of time-varying (TV) spectrum. The most widely adopted non-parametric approach is a short time Fourier transform (STFT), from which changes of mean frequency (MF) as well as other parameters for qualitative description of spectrum variation can be calculated. Similar idea of a sliding-window generalisation can also be used in case of parametric spectrum analysis methods. We applied such approach to obtain TV linear models of SEMGs, although its large variance due to independence of estimations in consequent windows represents a major drawback. This variance causes unrealistic abrupt changes in the curve of overall spectrum dynamics, calculated either as the second derivative of the MF or, as we propose, autoregressive moving average (ARMA) distance between subsequent linear models forming the TV parametric spectrum. A smoother estimation is therefore sought and another method shows to be superior over a simple sliding window technique. It supposes that trajectories of TV linear model coefficients can be described as linear combinations of known basis functions. We demonstrate that the later method is very appropriate for description of slowly changing spectra of SEMGs and that dynamics measures obtained from such estimations can be used as an additional indication of the fatigue process.