Table 1 Calculated features

1

Mean

\( \bar{x} = \frac{1}{N}\sum\nolimits_{n = 1}^{N} {x_{n} } \)

2

Peak to peak

\( x_{p - p} = \hbox{max} (x) - \hbox{min} (x) \)

3

Variation

\( x_{\text{var}} = \frac{1}{N}\sum\nolimits_{n = 1}^{N} {(x_{n} - \bar{x})^{2} } \)

4

Root mean square

\( x_{rms} = \sqrt {\frac{1}{N}\sum\nolimits_{n = 1}^{N} {x_{n}^{2} } } \)

5

Skewness

\( x_{skew} = \frac{1}{N}\sum\nolimits_{n = 1}^{N} {\left( {\frac{{x_{n} - \bar{x}}}{{\sqrt {x_{\text{var}} } }}} \right)}^{3} \)

6

Kurtosis

\( x_{kurtosis} = \frac{1}{N}\sum\nolimits_{n = 1}^{N} {\left( {\frac{{x_{n} - \bar{x}}}{{\sqrt {x_{\text{var}} } }}} \right)}^{4} \)

7

Crestor factor

\( x_{cf} = \frac{\hbox{max} (\left| x \right|)}{{x_{rms} }} \)

8

Impulse factor

\( x_{if} = \frac{\hbox{max} (\left| x \right|)}{{1/N\sum\nolimits_{n = 1}^{N} {\left| {x_{n} } \right|} }} \)

9

Mean of frequency

\( f_{p1} = \frac{{\sum\nolimits_{k = 1}^{K} {S_{k} } }}{K} \)

10

Variation of frequency

\( f_{p2} = \frac{{\sum\nolimits_{k = 1}^{K} {(S_{k} - f_{p1} )^{2} } }}{K - 1} \)

11

3rd moment of frequency

\( f_{p3} = \frac{{\sum\nolimits_{k = 1}^{K} {(S_{k} - f_{p1} )^{3} } }}{{K(\sqrt {f_{p2} } )^{3} }} \)

12

4th moment of frequency

\( f_{p4} = \frac{{\sum\nolimits_{k = 1}^{K} {(S_{k} - f_{p1} )^{4} } }}{{K(f_{p2} )^{2} }} \)

13

Energy ratio

\( ER = \frac{{\sqrt {1/N\sum\nolimits_{n = 1}^{N} {(d_{n} - \bar{d})^{2} } } }}{{\sqrt {1/N\sum\nolimits_{n = 1}^{N} {(y_{n}^{d} - \bar{y}^{d} )^{2} } } }} \)

14

FM0

\( FM0 = \frac{{PP_{x} }}{{\sum\nolimits_{h = 0}^{H} {P_{h} } }} \)

15

FM4

\( FM4 = \frac{{N\sum\nolimits_{n = 1}^{N} {(d_{n} - \bar{d})^{4} } }}{{[\sum\nolimits_{n = 1}^{N} {(d_{n} - \bar{d})^{2} ]^{2} } }} \)

16

M6A

\( M6A = \frac{{N^{2} \sum\nolimits_{n = 1}^{N} {(d_{n} - \bar{d})^{6} } }}{{[\sum\nolimits_{n = 1}^{N} {(d_{n} - \bar{d})^{2} ]^{3} } }} \)