TABLE 3.

Variables computed for EMG analysis

Time-domain features
Variable name	Abbreviation	Description	Equation
3rd Temporal Moment	TM3	Absolute value of cubed EMG signal	$TM3=\left|\frac{1}{k}{\displaystyle \sum }_{n=1}^k{x}_n^3\right|$
Absolute Value of Summation of Square Root	ABS_SQRT	Motion identification	$ABS\_SQRT=\left|{\displaystyle \sum }_{n=1}^k\sqrt{\left(x_n\right)}\right|$
			where k is the analysis window
Absolute Value of Summation of Exponential Root	ABS_EXP	Provides insight on the amplitude of the signal	$ABS\_\mathit{EXP}=\left|\frac{{\sum }_{n=1}^k{\left(x_n\right)}^{\mathit{exp}}}{k}\right|$
			where exp = 0.5, if ( n ≥ 0.25*k && n ≤ 0.75), else exp = 0.75. and k is the signal length
Average Amplitude Change	AAC	Average of the wavelength measurement	$AAC=\frac{1}{k}{\displaystyle \sum }_{n=1}^{k-1}\left|x_{n+1}-x_n\right|$
			where k is the signal length
Cardinality	CARD	Number of unique values within a set	Step 1: $y_n=sort\left(x_n\right)$
			Step 2: $CARD={\displaystyle \sum }_{n=1}^{k-1}\left|y_n-y_{n+1}\right|>ϵ$
			where ϵ = 0.01
Difference Absolute Mean Value	DABS_M	Modified MAV; estimated signal amplitude	$DABS\_M=\frac{1}{k}{\displaystyle \sum }_{n=1}^{k-1}\left|x_{n+1}-x_n\right|$
Difference Absolute Standard Deviation Value	DABS_SD	Modified standard deviation of the wavelength	$DABS\_SD=\sqrt{\frac{1}{k-1}{\displaystyle \sum }_{n=1}^{k-1}{\left(x_{n+1}-x_n\right)}^2}$
Difference Variance Value	DVAR	Modified VAR of EMG	$DVARV=\frac{1}{k-2}{\displaystyle \sum }_{n=1}^{k-1}{\left(x_{n+1}-x_n\right)}^2$
Enhanced Wavelength	ENH_WL	Enhanced wavelength	$ENH\_WL={\displaystyle \sum }_{n=2}^k\left|{\left(x_n-x_{n-1}\right)}^p\right|$
			where $p=\left(0.75,ifi\ge 0.2ki\le 0.8k\right)orp=\left(0.5\right)$
Enhanced Mean Absolute Value	ENH_MAV	Enhanced MAV	$ENH\_MAV=\frac{1}{k}{\displaystyle \sum }_{n=1}^k\left|x_n^p\right|$
			where $p=\left(0.75,ifi\ge 0.2ki\le 0.8k\right)orp=\left(0.5\right)$
Integrated EMG	INT_EMG	Summation of absolute value of signal amplitude	$INT\_EMG={\displaystyle \sum }_{n=1}^k\left|x_n\right|$
			where k is the signal length
Kurtosis	KURT	Statistical technique represent sharpness of distribution curve	$KURT=\frac{{\mu }_4}{{\sigma }^4}$
			where µ4 is the forth central moment, and is standard deviation
Log Coefficient of Variation	LOG_CoV	Logarithmic transformation of CoV	$\mathit{LOG}\_CoV=\mathit{log}\left(\frac{\sigma }{\mu }\right)$
Log Detector	LOG	Estimate of muscle contraction force	$\mathit{LOG}=e^{\frac{1}{k}{\sum }_{n=1}^k\mathit{log}\left(\left|x_n\right|\right)}$
Log Difference Absolute	LOG_DABS_M	Logarithmic transformation of DABS_M	$\mathit{LOG}\_DABS\_M=\mathit{log}\left(\frac{1}{k}{\displaystyle \sum }_{n=1}^{k-1}\left|x_{n+1}-x_n\right|\right)$
Mean Value
Log Difference Absolute Standard Deviation Value	LOG_DABS_SD	Logarithmic transformation of DABS_SD	$\mathit{LOG}\_DABS\_SD=\mathit{log}\left(\sqrt{\frac{1}{k-1}{\displaystyle \sum }_{n=1}^{k-1}{\left(x_{n+1}-x_n\right)}^2}\right)$
Log Teager Kaiser Energy Opertor	LOG_TK_EO	Measures instantaneous change in energy	$\mathit{LOG}\_TK\_EO=\mathit{log}({\displaystyle \sum }_{n=1}^{k-2}\left(x_n^2-\left(x_{n-1}\times x_{n+1}\right)\right)$
Maximum Fractal Length	MFL	Measures low level muscle activation	$MFL=lo{g}_{10}\left(\sqrt{{\displaystyle \sum }_{n=1}^{k-1}{\left(x_{n+1}-x_n\right)}^2}\right)$
Mean Absolute Deviation	MAD	Variation between real assessment and mean assessment	$MAD=\frac{1}{k}\left({\displaystyle \sum }_{n-1}^k\left|x_n-\overline{x}\right|\right)$
Mean Absolute Value	MAV	Average of absolute value of signal amplitude	$MAV=\frac{1}{k}{\displaystyle \sum }_{n=1}^k\left|x_n\right|$
Mean Value of Square Root	M_SQRT	Measure to estimate the total amount of activity in analysis window	$M\_SQRT=\frac{1}{k}{\displaystyle \sum }_{n=1}^k\sqrt{x_n}$
			where k is the signal length
Modified Mean Absolute Value	MAV1	Extension of MAV; wn is added for robustness	$MAV1=\frac{1}{k}{\displaystyle \sum }_{n=1}^k{w}_n\left|x_n\right|$
			where wn = 1, if 0.25*k ≤ n ≤ 0.75*k else, wn = 0.5
Modified Mean Absolute Value 2	MAV2	Improvements on MAV1; smoothness of robustness function	$MAV2=\frac{1}{k}{\displaystyle \sum }_{n=1}^k{w}_n\left|x_n\right|$
			where wn = 1, if 0.25*k ≤ n ≤ 0.75*k
			else wn = , if n < 0.25*k
			else wn = , otherwise
Myopulse Percentage Rate	MYOP	Average value of myopulse output	$MYOP=\frac{1}{k}{\displaystyle \sum }_{n=1}^k\left[f\left(x_n\right)\right]$
			where f(x) = 1 if x ≥ threshold, or f(x) = 0, otherwise. And threshold = 0.016
New Zero Crossing	NEW_ZC	Zero Crossing with improved threshold	$NEW\_ZC={\displaystyle \sum }_{n=1}^{k-1}f\left(x_i,x_{i+1}\right)$
			where $f\left(x_i,x_{x+1}\right)=\left(1,if{x}_i>Tand{x}_{i+1}<Torif{x}_i<Tand{x}_{i+1}>T\right)$ , otherwise $f\left(x_i,x_{x+1}\right)=0$
			and where $T=4\left(\frac{1}{10}{\displaystyle \sum }_{n=1}^{10}{x}_n\right)$
Root Mean Square	RMS	Root mean square of the signal	$RMS=\sqrt{\frac{1}{k}{\displaystyle \sum }_{n=1}^k{x}_n^2}$
Simple Square Integral	SSI	Energy index or the summation of squared signal amplitude	$SSI={\displaystyle \sum }_{n=1}^k{x}_n^2$
Skewness	SKEW	Skewness of the signal	$SKEW=\frac{{\sum }_{n=1}^k{\left(x_n-\overline{x}\right)}^3}{k-1\times {\sigma }^3}$
Slope Sign Change	SSC	Number of times the signal changes between -ve and +ve slopes	$SSC={\displaystyle \sum }_{n=1}^{k-1}\left[f\left[\left(x_i-x_{i-1}\right)\times \left(x_i-x_{i+1}\right)\right]\right]$
			where f(x) = 1, if x ≥ threshold, or f(x) = 0, otherwise. And threshold = 0.01
Standard Deviation	SD	Standard deviation of the signal	$SD=\sqrt{\frac{{\sum }_{n=1}^k{\left(x_n-\mu \right)}^2}{k}}$
Variance	VAR	Variance of the signal	$VAR=\frac{1}{k-1}\left({\displaystyle \sum }_{n-1}^k{\left(x_n-\overline{x}\right)}^2\right)$
Variance of EMG	VAR_EMG	Power index	$VAR\_EMG=\frac{1}{k-1}{\displaystyle \sum }_{n=1}^k{x}_n^2$
V-Order	V_O	Non-linear detector; similar in definition to RMS	$V\_O={\left(\frac{1}{k}{\displaystyle \sum }_{n=1}^k{x}_n^v\right)}^{\frac{1}{v}}$
			where V = 2
Waveform Length	WL	Measure of signal complexity; defined as cumulative length of waveform	$WL={\displaystyle \sum }_{n=1}^{k-1}\left|x_{n+1}-x_n\right|$
Willison Amplitude	W_AMP	Related to the firing of motor unit action potential	$W\_AMP={\displaystyle \sum }_{n=1}^{k-1}\left[f\left(\left|x_i-x_{i+1}\right|\right)\right]$
			where f(x) = 1, if x ≥ threshold, or f(x) = 0, otherwise. And threshold = 0.01
Zero Crossing	ZC	Number of times the amplitudes crosses zero amplitude level	$ZC={\displaystyle \sum }_{n=1}^{k-1}\left[sgn\left(x_n\times x_{n+1}\right)\cap \left|x_n-x_{n-1}\right|\ge threshold\right]$
			where sgn(x) = 1, if x ≥ threshold , or sgn(x) = 0, otherwise. And threshold = 0.01

Frequency-domain features
Variable name	Abbreviation	Description	Equation
Avarage Energy	AVE_E	Mean of the squared signal	$AVE\_E=\overline{\left(x^2\right)}$
Interquartile Range	IQR	Divergence regarding 75th and 25th percentile of the group	$IQR=Q_3-Q_1$
			where Q1 refers to first quartile, and Q3 refers to third quartile

Dimensionless feature
Variable name	Abbreviation	Description	Equation
Coefficient of variation	CoV	Quantifies the degree of variability of the signal with respect to mean	$CoV=\frac{\sigma }{\mu }$
			where µ is the mean of the signal, is standard deviation