# Support Vector Machine-Based EMG Signal Classification Techniques: A Review
## Appendix A Common Features
### Frequency Domain  
* Mean Frequency (MNF) It is a mean frequency which is calculated as the sum of the product of the MES signal power spectrum and the frequency divided by the total of the spectrum intensity [23]. In addition, it is known as central frequency or spectral center of gravity [38]. \[\text{MNF}=\frac{\sum_{l=1}^{M}{f_{l}P_{l}}}{\sum_{l=1}^{M}{P_{l}}},\] (27) where \(f_{l}\) is the spectral frequency in the bin of frequency \(l\), \(P_{l}\) is the EMG signal power spectrum in the bin \(l\), and \(M\) is the frequency bin length. * Median Frequency (MDF) It is the frequency divided into two regions with the same amplitude; that is to say, MDF is the total power average [23], and could be expressed as the number MDF with the property that \[\sum_{l=1}^{\text{MDF}}{P_{l}}=\sum_{l=\text{MDF}}^{M}{P_{l}}=\frac{1}{2}\sum _{l=1}^{M}{P_{l}},\] (28) where \(P_{l}\) is the EMG signal power spectrum at a frequency bin \(l\), and \(M\) is the frequency bin length. * Peak Frequency (PKF) It is the frequency at which maximum power occurs, described by \[\text{PKF}=\text{max}(P_{l}).\] (29)
* Mean Power (MNP) MNP is the mean power of the EMG power spectrum. It is calculated as \[\text{MNP}=\frac{\sum_{l=1}^{M}{P_{l}}}{M}.\] (30)* Total Power (TTP) It is defined as an aggregate of the EMG signal frequency spectrum or as zero spectrum moment, and is given by \[\text{TTP}=\sum_{l=1}^{M}P_{l}.\] (10)
* Frequency Ratio (FR) FR can be used to make a distinction between muscle contraction and relaxation [91], which uses the quotient obtained from the division of low-frequency EMG components with high frequency. The equation that defines it is expressed by: \[\text{FR}=\frac{\sum_{l=\text{LLC}}^{\text{ULC}}P_{l}}{\sum_{l=LHC}^{ \text{ULC}}P_{l}},\] (11) where ULC and LLC are upper and lower coefficients of the cutoff frequency of the low band frequency and UHC and LHC are those from the high frequency, respectively. The threshold to divide between low and high frequencies can be determined of two different ways, the first suggested by [PERSON] et al. [92], who used a range of 30-250 Hz for low frequency and 250-1000 Hz of high frequency. The values were obtained by experiments. The second was suggested by [PERSON] and [PERSON] [91], who proposed obtaining the frequency rates based on the MNF value. * Power Spectrum Ratio (PSR) The PSR can be defined as an extended version of the PKF and the FR [93]. It is the quotient between \(P_{0}\) that is close to the maximum value of MES power spectrum and \(P\) that is the total energy of MES power spectrum. It can be defined mathematically by \[\text{PSR}=\frac{P_{0}}{P},\] (12) where \[P_{0}=\sum_{l=f_{0}-n}^{f_{0}+n}P_{l}\quad\text{and}\quad P=\sum_{l=-\infty}^{ \infty}P_{l},\] with \(f_{0}\) the PKF value and \(n\) the MES integral limit. [PERSON] and [PERSON] [93] defined \(n=20\) and \(P\) in 10 and 500 Hz. * The First, Second and Third Spectral Movements Another statistic that is offered to MES spectral power analysis is the moment spectral. The first three moments are the most important [38]. These are calculated by \[\text{SM1}=\sum_{l=1}^{M}P_{l}f_{l},\] \[\text{SM2}=\sum_{l=1}^{M}P_{l}f_{l}^{2}\quad\text{and}\] (13) \[\sum_{l=1}^{\text{MDF}}{P_{l}}=\sum_{l=\text{MDF}}^{M}{P_{l}}=\frac{1}{2}\sum _{l=1}^{M}{P_{l}},\]0
* Variance of Central Frequency (VCF)It is defined by the use of some moment spectral and is written as \[\sum_{l=1}^{\text{MDF}}{P_{l}}=\sum_{l=\text{MDF}}^{M}{P_{l}}=\frac{1}{2}\sum _{l=1}^{M}{P_{l}},\]1 (100) where \(f_{c}\) is the central frequency. * Power Spectral Density (PSD) It is defined as the energy distribution or power signal over the different frequencies of which it is formed. Mathematically, it is defined as \[\sum_{l=1}^{\text{MDF}}{P_{l}}=\sum_{l=\text{MDF}}^{M}{P_{l}}=\frac{1}{2}\sum _{l=1}^{M}{P_{l}},\]2 (101) where \(X(f)\) is the \(x(t)\) Fourier Transform; the integral of this function in the whole axis \(f\) is the total energy value of \(x(t)\), the signal.