**2. Principle and theory of mean and median frequencies**

Frequency-domain or spectral-domain features are usually used in the assessing muscle fatigue and analysing MU recruitment (Oskoei & Hu, 2008). To transform the EMG signal in the time-domain to the frequency-domain, a Fourier transform of the autocorrelation function of the EMG signal is employed to provide the power spectrum (PS) or the power spectral density (PSD). Although PSD can be estimated by different methods, i.e. modern, parametric or model-based, the most commonly used PSD estimator in the EMG signal analysis is the Periodogram. It is defined as the square of absolute value of the Fourier transform of EMG signal divided by the signal length. Another stable and accurate PSD estimator is the autoregressive (AR) model (Zhang et al., 2010). Different kinds of statistical variables are applied to the PSD of EMG signal and the two popular used variables of PSD are mean and median. However, there are several possible statistical variables that can be applied to the PSD of EMG signal, such as summation or total, and peak value. Definitions of other statistical variables are presented in Section 2.2.
