Long-time Behavior of Surface Electromyography Time Series

We have previously reported that the mean-square displacement from the sEMG time series $x_{i}$ with $i=1,2,..., 2^{16}$ exhibits diffusive behavior for short times, $t \stackrel{<}{\sim} 50 \, \mbox{ms}$, which is followed by a plateau-like behavior for intermediate times, $50 \, \mbox{ms} \stackrel{<}{\sim} t \stackrel{<}{\sim} 500 \, \mbox{ms}$. For long times, $t \stackrel{>}{\sim} 500 \, \mbox{ms}$, the msd increases as time $t$ increases. We show that the long-time behavior reflects non-stationarity of the signal; we find that for a fixed time interval $t=\mbox{const}$, the displacement $X_{s,t} = \sum_{i=0}^{t-1} x_{s+i} \simeq \mu_{1} $ for $s \in [s_{0}, s_{1}]$ and $X_{s,t} = - \mu_{2}$ for $s \notin [s_{0}, s_{1}]$. This property explains the fit of the probability distribution $p_{t} ( X) = \left< \delta ( X - X_{s,t} )\right>_{s}$ as a superposition of two Gaussians that we reported in Physica A {\bf 386}, 698-709 (2007). Supported by a grant from the Research Corporation [UZ].