Table 1 Mathematical definitions of the features used in this study

Mean absolute value (MAV)

[25]

Variance (VAR)

[25]

Wave length (WL)

[25]

Wavelet denoise (WDEN)

θ = σ (0.3936 + 0.1829log₂(N)), σ-standard deviation of noise

Symmlet 7 mother wavelet, and hard threshold (θ).

[28, 29]. Finally the feature is MAV of denoised signal.

Energy based on discrete Fourier transformation (DFT)

,

where X [k] is DFT of x [n]

[25]

Autoregressive coefficients (AR)

The forward-backward approach. The sum of a least squares criterion for a forward model and the analogous criterion for a time-reversed model is minimized [27].

Cepstral coefficients (CEPS)

c₁ = -a₁

The cepstrum coefficients (c_i), are calculated from AR coefficients (AR model with order P), as proposed in Kang's work [26].

Autocorrelation-based, second order processing (HOS2)

,

H₀-noise only (null hypotesis), H₁-presence of signal

Toepliz matrix creation, based on estimate of autocorrelation; singular value decomposition; difference among maximum and minimum eigenvalue (σ) [21].

Cumulant-based third order processing (HOS3)

,

H₀-noise only, H₁-presence of signal

Toepliz matrix creation, based on estimate of third order cumulant of a data frame; singular value decomposition; the largest eigenvalue (λ) [21].

Autocorrelation minimum value (ACORR)

,

L-length of ROW

First negative peak value of r(τ) [23, 24].