## 3 Materials and Methods
### Methods  
First, the not a number (NaN) was removed all along the signals to maintain the alignment in each subject. Contrary to ECG and ABP signals, which were not normalized, the PPG data were subsequently subjected to normalization because it was originally in a different value range across each subject. The ECG and the ABP were not normalized because of the risk of losing the original signal units (mmHg) form and the aim of extracting morphological and temporal characteristics. In the next stage, the ECG, PPG, and ABP data were subjected to the low-frequency wavelet technique to remove breathing artifacts or a wandering baseline in the signals (Figure 1) by discarding the last 4 detail wavelet transform coefficients and the approximation coefficient, utilizing the Daubechies 8 mother wavelet with 10 decomposition levels, similar to the approach outlined in [33]. This denoising method was adopted mainly due to a better phase response, computational efficiency, and adaptivity to these biological signals. The whole preprocessing method adopted in this study is resumed in the following lines:  
* ECG, PPG, and ABP signal lengths are equal to 2 h.
* In the first step, we remove NaN. * In the second step, we perform wavelet denoising for low frequency with N = 10 and dB8. * Window segmentation length is 20 s for N = 292. * In the final step, QRS-PPG-ABP window segmentation (N = 7057). Furthermore, the original signal's mean was added to the one filtered to avoid the loss of inherent offset for the PPG data. By doing so, the morphological and physiological meaning of the Pulse Input Response (PIR) feature will be preserved. PIR is related to the maximum and minimum intensity of the PPG signal within a cardiac cycle. After the 2 signals are cropped into 20 s segments, they are subjected to a threshold. Segments whose minimum or maximum values are below or above the specified threshold are automatically eliminated. In such cases, the lower and the upper thresholds can be computed as  
\[threshold_{k}=\mu_{k}+a\sigma_{k}\;\;a>0 \tag{1}\]  
where \(a\) is the adjusted positive scalar of each signal subject. \(\Sigma_{k}\) and \(\mu_{k}\) are the signal \(k\)'s mean and standard deviation (STD), respectively. Anytime a signal's segment is discarded, segments in the same time interval are also discarded to preserve the alignment. The following procedure was to perform high-frequency wavelet denoising on each 20 s window obtained in the previous step. This process utilized the Daubechies 8 mother wavelet, employed 10 decomposition levels, and applied the soft Rigrsure thresholding approach, with threshold rescaling derived from noise estimates of the first-level coefficients. The Wavelet Toolbox function _wden.m_ in MATLAB was employed to perform this operation. The final processing step involves segmenting 20 s windows of denoised PPG, ABP, and ECG signals into smaller segments with fewer cardiac cycles for our feature extraction functions (see Figure 2). To achieve this, we applied a 4-level wavelet decomposition using the Symlets4 mother wavelet to the ECG signal within each 20 s window. As a result, the R peaks in the ECG signal become highly noticeable and prominent after the reconstruction of the second and third detail coefficients. This phase of our experiment is consistent, as it allows us to precisely determine the time location of the R peaks within each window, thereby exempting the need to detect large P and T waves abnormally. After detecting the R peaks, all three signals were once again segmented into different sets of corresponding intervals. These intervals consist of three PPG pulses: the preceding pulse, the ongoing pulse, and the initial part of the subsequent pulse. Figure 1: Low-frequency ECG–PPG and ABP signal denoised from subjects. The features necessitating peak detection were obtained using the MATLAB function _findpeaks.m_, configured with appropriate minimum peak height and minimum peak-to-peak distance settings.