# Table 3 Features extracted from the compiled datasets

Feature Equation
Average signal magnitude $$\frac{1}{N}\sum\nolimits _{i=1}^{N}\sqrt{x_i^2 + y_i^2 + z_i^2}$$
Maximum value $${\text {max}}({\mathbf {x}})$$
Minimum value $${\text {min}}({\mathbf {x}})$$
Mean ($$\bar{x}$$) $$\frac{1}{N} \sum\nolimits _{i=1}^{N} x_i$$
Standard deviation ($$\sigma _x$$) $$\sqrt{ \frac{1}{N} \sum\nolimits _{i=1}^{N}(x_i - \bar{x})^2}$$
Variance $$\sigma^2_x$$
Skewness $$\frac{\frac{1}{N} \sum \nolimits_{i=1}^{N} (x_i - \bar{x})^3}{\sigma^3_x}$$
Kurtosis $$\frac{\frac{1}{N} \sum\nolimits _{i=1}^{N} (x_i - \bar{x})^4}{\sigma^4_x}$$
Energy $$\frac{1}{N} \sum\nolimits _{i=1}^{N} |X_i|^2$$
Spectral entropy $$\sum\nolimits _{i=1}^{N} P(x_i) \log \frac{1}{P(x_i)}$$
Pairwise correlation between the axes $$\frac{{\hbox {cov}}({{\mathbf {x}}}, {{\mathbf {y}}})}{\sigma_x \sigma_y}$$
1. Each frame consists of N sequential samples, and x denotes a vector of these samples for each accelerometer axis, x, y and z. The FFT of x is denoted by X and the normalised power spectrum of x by $$P({\mathbf {x}})$$. Cross-correlation is calculated for each axis pair (xy), (xz), and (yz). All features except average signal magnitude provide three values: one per axis