## 2 Materials and Methods
### Signal Processing Features
#### 2.1.4 Statistical Features  
The statistical features investigated in this study are summarized in Table 5.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Feature** & **Description** & **Formula** \\ \hline Wavelet Bandwidth (WB) & The relative energy contribution in a time–frequency band [53] & \([cA,cD]=\text{dwt}(x^{\prime},db1^{\prime})\); \\  & & \(\text{m}=\frac{cA^{\prime}\cdot cA}{cA^{\prime}\cdot cA+cD^{\prime}\cdot cD}\) \\ \hline Wavelet Entropy Rate (ER) & Wavelet entropy represents signal disorder in the time–frequency domain [53; 58; 59] & \(\text{ER}=-\sum\text{possibility}_{\text{unique freq}}\times\log_{2}(\text{possibility}_{\text{unique freq}})\) \\ \hline \hline \end{tabular}  
Notes: \(x\) is the input signal. \(\text{dwt}(x^{\prime},db1^{\prime})\) performs a one-level discrete wavelet transform using Daubechies 1 (’db1’) wavelet. \(cA\) and \(cD\) are the approximation and detail coefficients, respectively. \(cA^{\prime}\) and \(cD^{\prime}\) represent the transposes. The dot product \(cA^{\prime}\cdot cA\) estimates the energy of approximation coefficients, as \(cD^{\prime}\cdot cD\) does for detail coefficients. In the entropy rate formula, \(\text{prob}_{i}\) is the normalized probability of the \(i\)th wavelet coefficient or band.  
\end{table}
Table 4: Wavelet-domain features extracted from the signal.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Feature** & **Description** & **Formula** \\ \hline Average Power (AvgPower) & The mean of the total power underneath the curve of the PSD estimate for a signal [39; 50] & AvgPower \(=\frac{\text{TotalSignalPower}}{\text{Signal Bandwidth}}\) \\ \hline Ratio of Spectral Peak (Welch, FFT, DCT) (RSP) & Ratio of the energies of low- and high-frequency bands [39; 50] & \(\text{RSP}=\frac{\max(\text{power}_{\text{freq}})}{\text{mean}(\text{power}_{ \text{freq}})}\) \\ \hline Signal-to-Noise Ratio (SNR) & Power of the whole signal over the power of its computed noise [39] & SNR \(=\frac{\text{Power}_{\text{signal}}}{\text{Power}_{\text{noise}}}\) \\ \hline Total Harmonic Distortion (THD) & Distortion of the whole signal compared to its harmonics [39] & THD \(=\frac{\sqrt{\sum_{n=2}^{N}P_{n}}}{P_{1}}\) \\ \hline Energy in Band 0.5 to 3 Hz (EB (0.5–3 Hz)) & Energy in a frequency band describing parts of distinct frequencies in the signal [54] & EB(0.5–3 Hz) \(=\int_{0.5}^{3}|X(f)|^{2}\,df\) \\ \hline Windowed Energy in Band 0.5 to 3 Hz (WEB) & Energy in a frequency band of 5 s windows with an overlap of 2.5 s, averaged from complete signal sequence [54] & WEB \(=\frac{1}{M}\sum_{i=1}^{M}\int_{0.5}^{3}|X_{i}(f)|^{2}\,df\) \\ \hline Peak Frequency (PeakFreq.) & The maximum spectral power [53] & PeakFreq. \(=\arg\max|X(f)|\) \\ \hline Spectral Centroid (SP) & The frequency that divides the spectral power distribution into two equal parts [53] & SP \(=\frac{\sum_{f}f|X(f)|^{2}}{\sum_{f}|X(f)|^{2}}\) \\ \hline Bandwidth (B) & Difference between the uppermost and lowermost frequencies in the signal [53] & \(B=\sqrt{\frac{\sum_{f=0}^{F}(f-\text{SP})^{2}\cdot P(f)}{\sum_{f=0}^{F}P(f)}}\) \\ \hline Regression Line for Windowed Energy (y) & Regression line of energy values from a window (2.5 s) moved through a signal sequence [54] & \(y=mx+b\) \\ \hline \hline \end{tabular}  
\end{table}
Table 3: Frequency-domain features extracted from accelerometer data.  
In total, 27 out of 30 introduced features were investigated for this study.