# Support Vector Machine-Based EMG Signal Classification Techniques: A Review
## Appendix A Common Features  
### Time Domain  
* Average Amplitude Value (AAV) AAV is the average amplitude from an EMG signal [80]. The principal problem with this feature is that the amplitude from the signal also varies with sweat or any other factor producing skin conductance changes [81]. For a segment of \(N\) samples, it is given by \[\text{AAV}=\frac{1}{N}\sum_{k=1}^{N}x_{k},\] (1) where \(x_{k}\) is the \(k\)-th sample. * Mean Absolute Value (MAV) MAV is one of the most used statistics in signal analysis [27], and it can be described as \[\text{MAV}=\frac{1}{N}\sum_{k=1}^{N}|x_{k}|.\] (2)
* Modified Mean Absolute Value type 1 (MMAV1) This is a MAV generalization [82] where a weighted window function \(w_{k}\) is used in the MAV equation with the purpose to make it more robust; it is computed as \[\text{MMAV1}=\frac{1}{N}\sum_{k=1}^{N}w_{k}|x_{k}|,\] (3) where \[w_{k}= \begin{cases}1,&0.25\leq k\leq 0.75N,\\ 0,&\text{otherwise.}\end{cases} \] (4)* Modified Mean Absolute Value type 2 (MMAV2) This is another MAV generalization, such as MMAV1 [82], where the weight function \(w_{k}\) is continuous, which improves the smoothness of the weighted function. It is given by \[\text{MMAV2}=\frac{1}{N}\sum_{k=1}^{N}w_{k}|x_{k}|,\] (11) where \[w_{k}= \begin{cases}1,&0.25\leq k\leq 0.75N,\\ 4k/N,&k<0.25N,\\ 4(N-k)/N,&\text{otherwise}.\end{cases} \]
* Simple Square Integral (SSI) This feature corresponds to the signal energy [38], that is, SSI is the sum of squared values of the EMG signal amplitude, it can be expressed as: \[\text{SSI}=\sum_{k=1}^{N}x_{k}^{2}.\] (12)
* Variance (VAR) This statistic is another power index [52], and is defined as the mean of the squared values of the deviation from the mean of the variable; it can be expressed as \[\text{VAR}=\frac{1}{N-1}\sum_{k=1}^{N}x_{k}^{2}.\] (13)
* Zero Crossings (ZC) A simple measure of frequency can be obtained by counting the number of times that the wave crosses by zero [27]. To reduce the noise effects, a lower bound for the absolute difference could be included as a threshold \(L\). Given two consecutive samples \(x_{k}\) and \(x_{k+1}\), ZC is the count of the zero crossings, that is, \[\text{ZC}=\sum_{k=1}^{N-1}f_{ZC}(x_{k}),\] (14) where \[f_{ZC}(x_{i})= \begin{cases}1,&x_{i}x_{i+1}<0\text{ and }\\ &|x_{i}-x_{i+1}|\geq L\\ 0,&\text{otherwise}.\end{cases} \] This algorithm will fail to log a zero crossing if the absolute difference of two consecutive samples of opposite sign are lower than the selected threshold. * Slope Sign Changes (SSC) This feature allows another description of the frequency; it is the number of times that a slope sign change occurs [27]. Again, an adequate threshold can be chosen to reduce the induced noise. Given three consecutive samples \(x_{k-1}\), \(x_{k}\) and \(x_{k+1}\), the SSC count is increased if \[\text{SSC}=\sum_{i}f_{\text{SSC}}(x_{i}),\] (15)where \[f_{\text{SSC}}(x_{i})= \begin{cases}1,&\text{if }x_{i}<x_{i+1}\text{ and }x_{i}<x_{i-1}\\ &\text{or }x_{i}<x_{i+1}\text{ and }x_{i}>x_{i-1},\\ 0,&\text{otherwise}.\end{cases} \]
* Waveform Length (WL)  WL provides information about the complexity of the waveform in each segment [27]; this is simply the accumulated waveform length above time segment defined as \[\text{WL}=\sum_{k=1}^{N}|x_{k}-x_{k-1}|.\] (11)
* Average Amplitude Change (AAC)  AAC is the mean value of the absolute difference between two consecutive samples [80], that is, \[\text{AAC}=\frac{1}{N}\sum_{k=1}^{N}|x_{k+1}-x_{k}|.\] (12)
* Willson Amplitude (WAMP)  WAMP is an EMG signal frequency information measure. It is the number of times the amplitude of the absolute difference between two contiguous samples exceeds a preset lower bound \(L\). This is related with the triggering of the action potentials of motor unit and muscle contraction force. It is defined as \[\text{WAMP}=\sum_{k=1}^{N-1}f(|x_{k+1}-x_{k}|),\] (13) where \[f(x)= \begin{cases}1,&\text{if }x>L,\\ 0,&\text{otherwise}.\end{cases}