Table 3 Features extracted from the compiled datasets

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

\(\frac{{\hbox {cov}}({{\mathbf {x}}}, {{\mathbf {y}}})}{\sigma_x \sigma_y}\)