Table 2.

Proposed set of statistical time domain features estimated from the frequency spectra during the signal processing in the FD analysis, where each z(i) is a spectrum for i = 1, 2,…,Q, and Q is the total number of lines for an estimated spectrum; f_q(i) is the frequency value of the i-th spectrum line.

Statistical Feature	Mathematical Equation
Mean	$f_1=\frac{1}{Q} {\displaystyle \sum }_{i=1}^{Q}z\left(i\right)$	(24)
Variance	$f_2=\frac{1}{Q-1} {\displaystyle \sum }_{\mathrm{i}=1}^Q{\left(z\left(i\right)-f_1\right)}^2$	(25)
Third moment	$f_3=\frac{1}{Q{\left(\sqrt{f_2}\right)}^3} {\displaystyle \sum }_{i=1}^Q{\left(z\left(i\right)-f_1\right)}^3$	(26)
Fourth moment	$f_4=\frac{1}{Q{\left(\sqrt{f_2}\right)}^2} {\displaystyle \sum }_{i=1}^Q{\left(z\left(i\right)-f_1\right)}^4$	(27)
Grand mean	$f_5=\frac{{{\displaystyle \sum }}_{i=1}^Q{f}_q\left(i\right) z\left(i\right)}{{{\displaystyle \sum }}_{i=1}^{Q}z\left(i\right)}$	(28)
Standard deviation 1	$f_6=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^Q{\left(f_q\left(i\right)-f_5\right)}^{2}z\left(i\right)}{Q}}$	(29)
C Factor	$f_7=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^Q{f}_q{\left(i\right)}^2 z\left(i\right)}{{{\displaystyle \sum }}_{i=1}^{Q}z\left(i\right)}}$	(30)
D Factor	$f_8=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^Q{f}_q{\left(i\right)}^4 z\left(i\right)}{{{\displaystyle \sum }}_{i=1}^Q{f}_q{\left(i\right)}^2 z\left(i\right)}}$	(31)
E Factor	$f_9=\frac{{{\displaystyle \sum }}_{i=1}^Q{f}_q{\left(i\right)}^2 z\left(i\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^{Q}z\left(i\right) {{\displaystyle \sum }}_{i=1}^Q{f}_q{\left(i\right)}^4 z\left(i\right)}}$	(32)
G Factor	$f_{10}=\frac{f_6}{f_5}$	(33)
Third moment 1	$f_{11}=\frac{{{\displaystyle \sum }}_{i=1}^Q{\left(f_q-f_5\right)}^3 z\left(i\right)}{Q f_6^3}$	(34)
Fourth moment 1	$f_{12}=\frac{{{\displaystyle \sum }}_{i=1}^Q{\left(f_q\left(i\right)-f_5\right)}^4 z\left(i\right)}{Q f_6^4}$	(35)
H Factor	$f_{13}=\frac{{{\displaystyle \sum }}_{i=1}^Q{\left(f_q\left(i\right)-f_5\right)}^{1/2} z\left(i\right)}{Q \sqrt{f_6}}$	(36)
J Factor	$f_{14}=\frac{\left(f_7+f_8\right)}{f_1}$	(37)