Statistical Feature

Formula

1

Wilson Amplitude (WAMP): This is the number of times that the difference between two consecutive amplitudes exceeds a certain threshold. T = 0.05.

$\text{WAMP}={\displaystyle \sum _{i=1}^{N}u\left(\left|x_{i+1}-x_i\right|-T\right)}$

2

Zero Crossing (ZC): ZC represents the number of times that the amplitude of the signal passes through zero. Because the arithmetic of the ZCR is uncomplicated and easy to implement. The ZCR is defined as the number of zero-crossings in a fixed data length. A threshold must be included in the ZCR calculation to reduce the zero-crossings induced by measurement noise.

$\text{ZC}={\displaystyle \sum _{i=1}^{N-1}u\left(-x_i{x}_{i+1}\right)}$

3

Mean of Amplitude (MAV): This feature determines the mean of the difference in amplitudes of two consecutive samples.

$\text{MAV}=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left|x_i\right|}$

4

Mean Frequency (MNF): This feature estimates the mean frequency of the signal in a time segment. MNF is the average frequency value obtained by dividing the power spectrum density values of each frequency of the signal and the multiplication of the frequencies by the total power spectrum density. The $h_i$ value refers to the frequency value in the i-frequency spectrum, and $f_i$ likewise refers to the power spectrum.

$\text{MF}=\frac{{\displaystyle {\sum }_{i=1}^N{h}_i{f}_i}}{{\displaystyle {\sum }_{i=1}^N{h}_i}}$

5

Median Frequency (MDF): MDF is the frequency value in the middle of the two halves of the spectrum. The median in the spectrum is known as the frequency.

$\text{MDF}={\displaystyle \sum _{j=1}^{\text{MDF}}{P}_j}={\displaystyle \sum _{j=\text{MDF}}^M{P}_j}=\frac{1}{2}{\displaystyle \sum _{j=1}^M{P}_j}$

6

Variance (VAR): In the stochastic process, variance characterizes the average power of a random signal and can be explained as follows.

$\text{VAR}=\frac{1}{N-1}{\displaystyle \sum _{i=1}^N{x}_i^2}$

7

Average Amplitude Coupling (AAC): The AAC parameter is considered equivalent to the wavelength (WL) value of the signal, except that the wavelength of the signal is averaged.

$\text{AAC}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N-1}\left|X_{i+1}-X_i\right|}$

8

Difference Absolute Standard Deviation (DASD): This parameter’s value is similar to the RMS characteristic, in other words, it is the standard deviation value of the wavelength.

$\text{DASDV}=\sqrt{\frac{1}{N-1}}{\displaystyle \sum _{i=1}^{N-1}{\left(X_{i+1}-X_i\right)}^2}$

9

Wavelet Length Power (WL): this statistical feature is based on computing the Euclidian length of the waves within the time series.

$\text{WL}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N-1}\left|X_{i+1}-X_i\right|}$

10

Log value (LOG): This parameter computes the natural logarithmic of particular time series.

$\text{LOG}={\text{e}}^{\frac{1}{N}{\displaystyle {\sum }_{i=1}^N\log \left|X_i\right|}}$

11

Slope Sign Change (SSC): It is another method to represent the frequency information of the signal. To avoid background noise in the signal by changing the sign of the signal slope several times, the positive and negative slopes between three consecutive segments are determined by using the threshold function to determine the number of changes.

$\text{SSC}={\displaystyle \sum _{i=2}^{N-1}\left[f\left(X_i-X_{i-1}\right)\ast \left(X_i-X_{i+1}\right)\right]}$ ;

$f\left(X\right)=\{\begin{array}{l}1,\text{if}X\ge \text{thresholdvalue}\\ 0,\text{otherwise}\end{array}$

12

Root Mean Square (RMS): It is the effective value of the amplitude values of a signal. As expressed in Equation, it means the square root of the average of the squares of the values of the N-length X signal at point i. Numerical values containing the RMS and standard deviation (SD) characteristics of the signal at the time of contraction increase significantly. The RMS is also known as the quadratic mean and is a particular case of the generalized mean with exponent 2.

$\text{RMS}=\sqrt{\frac{1}{n}{\displaystyle \sum _i{x}_i^2}}$

13

Standard Deviation (SD): A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out.

$\sigma =\sqrt{\frac{{{\displaystyle \sum }}^{\text{}}{\left(x_i-\mu \right)}^2}{N}}$