# Analysis of Surface EMG Parameters in the Overhead Deep Squat Performance
## 2 Materials and Methods
### Investigated Parameters Description
#### 2.2.1 Maximum Voluntary Contraction
\[X=\{x[n],x[n-1],...x[n-(M\)\(W\)L\(-\)\(1)]\}, \tag{1}\]  
where \(x\) is an absolute value of a sEMG signal sample, \(n\) is the number of samples, and \(M\)\(W\)L is the moving window length. Next, the four most numerous bins are found, and the vector \(D\) of the sEMG samples (\(d[i]\), for \(i\in\{k,k-1...,(K-1)\}\), where \(K<M\)\(W\)L ) belonging to the detected most numerous bins, is created. The mean value of \(D\) is the output of MAHF. The principle of the operation of MAHF is presented in Figure 6. After the filtering stage, the signal was processed using a moving root mean square (MRMS) with a window length of 150 ms. In the next step, the variance analysis of the processed sEMG derivative was used to determine muscle excitation levels. The details of the threshold process are given below. Figure 4: The block diagram of the used sEMG processing method. The first filters with a set of dedicated digital filters, the second is impulse interference removal, and the third is envelope calculation and MVC determining process. Figure 5: The magnitude response (blue line) and phase response (red line) of FIR filters: (**a**) 852-order band stop filter (50 Hz), (**b**) 266-order high-pass (10 Hz) filter, (**c**) 5-order low-pass (250 Hz) filter. Thresholding  
The processed sEMG signal representing muscle excitation was divided into 100 ms segments to determine the muscle excitation threshold. For each segment, the first derivative and the variance (the measure of dispersion) of the derivative are calculated to find the level of artifacts. Then, the mean (\(MD\)) and standard deviation values of variance (\(STDD\)) from whole segments of derivatives are calculated according to Formulas (2) and (3), respectively. \[MD=\frac{1}{N}\sum_{i=1}^{N}v_{i}, \tag{2}\]  
\[STDD=\sqrt{\sum_{i=1}^{N}\frac{(v_{i}-MD)^{2}}{N}}, \tag{3}\]  
where \(v_{i}\) denotes the variance of derivatives of i-th segments of sEMG signal for all (\(N\)) sEMG segments under consideration. (\(MD\)) and (\(STDD\)) values give information on sEMG amplitude changes. Based on the calculated \(MD\) and \(STDD\), the threshold level for detecting artifacts (\(TAL\)) is determined using the following formula:  
\[TAL=MD+sl\cdot STDD, \tag{4}\]  
where \(MD\) (2) and \(STDD\) (3) are the mean and standard deviation [30] of variance from the segments of derivatives, respectively, and \(sl\) is a constant that determines the sensitivity of artifact detection. In our case, \(sl\) was set to 0.95. Figure 6: The principle of the operation of MAHF. The seven-bin histogram of the sEMG data contained in the window (\(X=\{x[n],x[n-1],...,x[n-(MWL-1)]\}\)) of \(MWL\) length is calculated Next, the vector \(D\) of sEMG samples \(d[i]\), for \(i\in\{k,k-1...,(K-1)\}\), where \(K<MWL\), belonging to the four most numerous bins, is created. The mean value \(y[n]\) of \(D\) is the output of the filter. Figure reproduced with permission from [27]; copyright 2023 Wydawnictwo Politechniki Slaskiej. In the next step, the variance value of each segment is compared with \(TAL\). If the variance of the first derivative of a given segment exceeds \(TAL\), the analyzed segment of sEMG is marked as noisy and excluded from further analysis. Then, the maximum amplitude of sEMG signal (\(MAsEMG\)) is determined according to (5):  
Figure 5.0  
where \(x(n)\) is a processed discrete sEMG signal and \(K\) is the length of analyzed (not marked noisy) sEMG. In the further steps, all samples of the sEMG signal exceeding the determined maximum amplitude are ignored. The maximum value and time location are searched in the sEMG signal prepared in this way. Finally, a symmetric window of a \(2D\) (\(D=50\) ms) length is created relative to the found time location. The threshold value is defined as the mean of the sEMG signal in the assumed window and refers to the level of muscle excitation.