## 2 Materials and Methods
### Signal Processing Features
#### 2.1.1 Time-Domain Features  
The time-domain features explored in this work are summarized in Table 2.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Feature** & **Description** & **Formula** \\ \hline Number of Steps (numSteps) & The number of steps taken in a given time interval [39; 61] & - \\ \hline Average Step Time (AvgStepTime) & The average time elapsed for each step [39; 50] & \(AvgStepTime=\frac{\text{total time}}{\text{numSteps}}\) \\ \hline Average Cadence (AvgCad) & Ratio of total steps to total time [39; 61] & AvgCad = \(\frac{\text{numSteps}}{\text{total time}}\) \\ \hline Skewness (S) & Asymmetry of the signal distribution [39; 53; 61] & \(S=\frac{\frac{1}{\hbar}\sum\limits_{i=1}^{n}\left(x_{i}-x\right)^{3}}{\left( \frac{1}{\hbar}\sum\limits_{i=1}^{n}\left(x_{i}-x\right)^{2}\right)^{3/2}}\) \\ \hline Kurtosis (K) & Extent to which signal amplitudes lie predominantly on one side of the mean [39; 53; 61] & \(K=\frac{\frac{1}{\hbar}\sum\limits_{i=1}^{n}\left(x_{i}-x\right)^{4}}{\left( \frac{1}{\hbar}\sum\limits_{i=1}^{n}\left(x_{i}-x\right)^{2}\right)^{2}}\) \\ \hline Coefficient of Variation of Step & Standard deviation of stride interval divided by mean stride interval [53; 58] & \(CV_{\text{step}}=\sqrt{\frac{1}{N}\sum\limits_{i=1}^{N}\left(I_{i}-I\right)^{2} }\div I\) \\ \hline Harmonic Ratio (HR) & Quantities harmonic composition of accelerations via DFT [53; 62] & \(HR=\frac{\sum\limits_{n=24.6\ldots}^{n}A_{n}}{\sum\limits_{n=13.5\ldots}^{n}A_{ n}}\) \\ \hline Average Step Length (AvgStepLength) & The average distance covered per step [39; 50] & \(AvgStepLength=\frac{0.084}{AvgStepTime}+1.89\) \\ \hline Gait Velocity (gaitVelocity) & Ratio of total distance covered to total time [39; 61] & \(gaitVelocity=\frac{AvgStepLength}{AvgStepTime}\) \\ \hline Minimum and Maximum Difference (minMaxDiff) & Global max of a step minus global min, averaged over all steps [54] & \(\min\max\text{Diff}=\max(x)-\min(x)\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Time-domain features extracted from accelerometer data.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Feature Name** & **Applied Cases** & **Unit/Variable Type** \\ \hline Energy in Band 0.5-3 Hz & Parkinson’s Disease [54] & Energy (a.u.) \\ \hline Windowed Energy in Band 0.5-3 Hz & Parkinson’s Disease [54] & Energy (a.u.) \\ \hline Peak Frequency & Parkinson’s, Peripheral Neuropathy [53], Paraspinal [51] & Hertz (Hz) \\ \hline Spectral Centroid & Parkinson’s Disease, Peripheral Neuropathy [53] & Hertz (Hz) \\ \hline Bandwidth & Parkinson’s, Peripheral Neuropathy [53] & Hertz (Hz) \\ \hline Regression Line for Windowed Energy & Parkinson’s Disease [54] & Slope (dimensionless) \\ \hline Wavelet Bandwidth & Parkinson’s, Peripheral Neuropathy [53] & Hertz (Hz) \\ \hline Wavelet Entropy Rate & Parkinson’s, Dysphagia, Neural Control [58; 59] & Bits or dimensionless \\ \hline Zeroth-Lag Cross-Correlation Coefficient & Parkinson’s, Peripheral Neuropathy [53] & Correlation coefficient (\(-1\) to \(1\)) \\ \hline Lempel-Ziv Complexity & Parkinson’s, Peripheral Neuropathy [53], EEG [60] & Dimensionless (complexity score) \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._The time-domain features listed in Table 2 are extracted from accelerometer signals using statistical gait analysis methods. For instance, skewness and kurtosis characterize the distribution shape of the signal values, while step time and cadence capture temporal gait patterns. In these formulas, \(x_{i}\) denotes the \(i\)th sample in the time series, \(\bar{x}\) is the mean, \(I_{i}\) represents individual step intervals, and \(P(f_{i})\) is the probability of occurrence of a given feature pattern used for entropy calculation. The harmonic ratio (\(HR\)) is computed from the discrete Fourier transform (DFT) components to quantify gait symmetry. These features collectively quantify the variability, regularity, and rhythmicity of walking patterns under different conditions.