Table 2 Mathematical definition of EMG selected features

1

Absolute value of summation of exp. root (ASM) [16, 17]

\(ASM=\sum\limits_{i=1}^{L}|{({x}_{i})}^{P}|\)

\(P=\left\{\begin{array}{lc}0.5, if& i>0.25\ L\ and\ i<0.75\ L\\ \\ 0.75& otherwise\end{array}\right.\)

2

Absolute value of the summation of square root (ASR) [16, 17]

\(ASR=|\sum_{i=1}^{L}{({x}_{i})}^{1/2}|\)

3

Auto-regressive model (AR) [16, 18]

\({X}_{n}=\sum\limits_{i=1}^{p}{a}_{i}\left({X}_{n-1}\right)+{W}_{n}\)

Where Xn a sample of the model signal is, ai is the AR coefficients, wn is the white noise error term, and P is the order of the AR model

4

Average amplitude change (AAC) [16]

\(AAC=\frac{1}{L}\sum\limits_{i=1}^{L-1}|{X}_{i+1}-{X}_{i}|\)

5

Average power (AP) [17]

\(AP=\frac{1}{L}\sum\limits_{i=L}^{1}{({X}_{i})}^{2}\)

6

Cardinality (CARD) [16]

\(CARD=\sum\limits_{i=1}^{L-1}F({x}_{i})\)

\(Y=\ sort\ (x)\)

\(F\left({x}_{i}\right)=\left\{\begin{array}{lrl}1,& if& \left({|y}_{i}-{y}_{i+1}|>T\right)\\ \\ &0,& otherwise\end{array}\right.\)

\(Y=sort(x)\)7

Coefficient of variation (COV) [18]

\(COV=\frac{\sqrt{\frac{1}{L-1}\sum_{i=1}^{L}{({X}_{i})}^{2}}}{\frac{1}{L}\sum_{i=1}^{L}|{X}_{i}|}\)

8

Difference mean absolute value (DAMV) [17]

\(DAMV=\sqrt{\frac{\sum_{i=1}^{L-1}|{X}_{i}-{X}_{i+1}|}{L}}\)

9

Difference absolute standard deviation value (DASDV) [17]

\(DASDV=\sqrt{\frac{\sum_{i=1}^{L-1}{({X}_{i}-{X}_{i+1})}^{2}}{L-1}}\)

10

Difference variance value (DVARV) [18]

\(DVARV=\frac{1}{L-2}\sum\limits_{i=1}^{L-1}{({X}_{i+1}- {X}_{i})}^{2}\)

11

Enhanced mean absolute value (EMAV) [18]

\(EMAV=\frac{1}{L}\sum\limits_{i=1}^{L}|{({x}_{i})}^{P}|\)

\(P=\left\{\begin{array}{lc}1, if& i>0.2\ L\ and\ i<0.8\ L\\ \\ 0.5& otherwise\end{array}\right.\)

12

Enhanced wavelength (EWL) [17]

\(EWL=\frac{1}{L}\sum\limits_{i=2}^{L}|{({x}_{i}-{x}_{i-1})}^{P}|\)

\(P=\left\{\begin{array}{lc}1, if& i>0.2\ L\ and\ i<0.8\ L\\ \\ 0.5 & otherwise\end{array}\right.\)

13

Integrated EMG (IEMG) [16]

\(IEMG=\sum\limits_{i=1}^{L}|{X}_{i}|\)

14

Interquartile range (IQR) [16]

IQR = Q3–Q1

First quartile Q1 = median of the n smallest values

Third quartile Q3 = median of the n largest values

The second quartile Q2 is the same as the ordinary median

15

Kurtosis (KURT) [16]

\(KURT=L\frac{\sum_{i=1}^L\left(x_i-\bar{x}\right)^4}{\left(\sum_{i=1}^L\left(x_i-\bar{x}\right)^2\right)^2}\)

16

Log detector (LD) [16]

\(LD=\mathrm{exp}(\frac{1}{L}\sum\limits_{i=1}^{L}Log(\left|{X}_{i}\right|))\)

17

Log coefficient of variation (LCOV) [16]

\(LCOV=\mathrm{log}\frac{\sqrt{\frac{1}{L-1}\sum_{L}^{1}{({X}_{i})}^{2}}}{\frac{1}{L}\sum_{L}^{1}|{X}_{i}|}\)

19

Log difference mean absolute value (LDAMV) [16]

\(LDAMV=\mathrm{log}\sqrt{\frac{\sum_{i=1}^{L-1}|{X}_{i}-{X}_{i+1}|}{L}}\)

20

Log difference absolute standard deviation value (LDASDV) [17]

\(LDASDV=log\sqrt{\frac{\sum_{i=1}^{L-1}{({X}_{i}-{X}_{i+1})}^{2}}{L-1}}\)

21

Log Teager-Kaiser energy operator (LTKEO) [16]

\(LTKEO=log\sum\limits_{i=2}^{L-1}{({X}_{i})}^{2}-{X}_{i-1}\times{X}_{i+1})\)

22

Maximum fractal length (MFL) [16]

\(MFL=\mathrm{log}\sqrt{\sum\limits_{i=1}^{L-1}{\left({X}_{i+1}-{X}_{i}\right)}^{2}}\)

23

Mean absolute value (MAV) [17]

\(MAV=\frac{1}{L}\sum\limits_{i=1}^{L}|{X}_{i}|\)

24

Mean absolute deviation (MAD) [16]

\(MAD=\frac1L\sum\limits_{i=1}^L\left|\left(x_i-\bar{x}\right)\right|\)

25

Mean value of the square root (MSR) [16]

\(MSR=\frac{1}{L}\sqrt{\sum\limits_{i=1}^{L}{({X}_{i})}^{2}}\)

26

Modified mean absolute value (MMAV) [16]

\(MMAV=\frac{1}{L}\sum\limits_{i=1}^{L}{W}_{i}|{x}_{i}|\)

\(\left({W}_{i}\right)=\left\{\begin{array}{rr}1, if& 0.25\ L < i < 0.75\ L\\ \\ 0.5 & otherwise\ \ \end{array}\right.\)

27

Modified mean absolute value 2 (MMAV2) [18]

\(MMAV2=\frac{1}{L}\sum\limits_{i=1}^{L}{W}_{i}|{x}_{i}|\)

\({W}_{i}=\left\{\begin{array}{lr}1, & if\ 0.25\ L < i < 0.75\ L\\ \\ \frac{4i}{L}, & if\ i<0.25\\ \frac{4\left(i-L\right)}{L} &otherwise\end{array}\right.\)

28

Myopulse percentage rate (MYOP) [18]

\(MYOP=\frac{1}{L}\sum\limits_{i=1}^{L}F({x}_{i})\)

\(F\left({x}_{i}\right)=\left\{\begin{array}{ll}1, & if\quad \left({x}_{i}>T\right)\\ \\ \quad 0, & otherwise\end{array}\right.\)

29

New zero crossing (FZC) [16]

\(FZC=\sum\limits_{i=1}^{L-1}F({x}_{i})\)

\(T=\frac{4}{10}\sum\limits_{i=1}^{10}{x}_{i}\)

\(F\left({x}_{i}\right)=\left\{\begin{array}{lr}\ 1, if & \left({x}_{i} > T\ \&\ {x}_{i+1} < T \right)|\left({x}_{i} < T\ \&\ {x}_{i+1} > T \right)\\ \\ 0 & otherwise\end{array}\right.\)

30

Root mean square (RMS) [18]

\(RMS=\sqrt{\frac{1}{L}\sum\limits_{i=1}^{L}{({X}_{i})}^{2}}\)

31

Simple square integral (SSI) [16]

\(SSI=\sum\limits_{i=1}^{L}{({X}_{i})}^{2}\)

32

Skewness (SKEW) [16]

\(SKEW=\frac{\sum_{i=1}^L\left(x_i-\bar{x}\right)^3}{\left(L-1\right)\left(\sum_{i=1}^L\left(x_i-\bar{x}\right)^2\right)^3}\)

33

Slope sign change (SSC) [17]

\(SSC=\sum\limits_{i=2}^{L-1}F\left({x}_{i}\right)\)

\(F\left({x}_{i}\right)=\left\{\begin{array}{lr}\ \ 1, & if\ \left({x}_{i}>{x}_{i+1}\&\ {x}_{i}>{x}_{i-1} \right)|\left({x}_{i}<{x}_{i+1}\& {x}_{i}<{x}_{i-1} \right)\\ \\ 0 & otherwise\end{array}\right.\)

34

Standard deviation (SD) [16]

\(SD=\sqrt{\frac{1}{L-1}\sum\limits_{i=1}^{L}{({X}_{i})}^{2}}\)

35

Temporal Moment (TM) [16]

\(TM=\left|1/L\sum\limits_{i=1}^L\left(X_i\right)^3\right|\)  

36

Variance (VAR) [16]

\(VAR=\frac{1}{L-1}\sum\limits_{L}^{1}{({X}_{i})}^{2}\)

37

VOrder (VO) [16]

\(VO={Y}^\frac{1}{4}\)

\(Y=\frac{\sum_{i=1}^{L}{\left({X}_{i}\right)}^{4}}{L}\)

38

Wavelength (WL) [16]

\(WL=\sum\limits_{i=2}^{L-1}|{X}_{i}-{X}_{i-1}|\)

39

Willison amplitude (WA) [17]

\(WA=\sum\limits_{i=1}^{L-1}F({x}_{i})\)

\(F\left({x}_{i}\right)=\left\{\begin{array}{ll}1, & if\quad \left({|x}_{i}-{x}_{i+1}|>T\right)\\ \\ 0, &\quad otherwise\end{array}\right.\)

40

Zero crossing (ZC) [16]

\(ZC=\sum\limits_{i=1}^{L}F({x}_{i})\)

\(F\left({x}_{i}\right)=\left\{\begin{array}{lr}\ 1, & if\ \left({x}_{i}>0\ \&\ {x}_{i+1}<0 \right)|\left({x}_{i}<0\ \&\ {x}_{i+1}>0 \right)\\ \\ 0 &otherwise\end{array}\right.\)