## 2 Description of the Proposed Method
### PPG Signal Description, Analysis, and Processing  
The PPG signal together with its derived parameters (particularly HR and ORI) describe the current state of the human vascular system and, in this way, they can be used for detection and quantification of the stress level [7]. Generally, in a PPG cycle, two maxima (systolic and diastolic) provide valuable information about the pumping action of the heart. For description of signal properties of the sensed PPG waves the energetic, time, and statistical parameters are determined. The sensed PPG signal representation is typically in the absolute numerical range \(A_{\text{NR}}\) given by the used type of an analog-to-digital (A/D) converter, e.g., output values of the 14-bit A/D converter have a relative unipolar representation in the range from 0 to 16,192 (=\(2^{14}=A_{\text{NR}}\)). First, from this absolute PPG signal, the local maximum \(Lp_{\text{MAX}}\) and local minimum \(Lp_{\text{MIN}}\) levels of the peaks corresponding to the heart systolic pulses are determined to obtain the mean peak level \(Lp_{\text{MEAN}}\). Then, the mean signal range \(PPG_{\text{RANGE}}\) is calculated from the global minimum (offset level \(L_{\text{OFS}}\)) and \(A_{\text{NR}}\) by the equation  
\[PPG_{\text{RANGE}}=(Lp_{\text{MEAN}}-L_{\text{OFS}})/\text{A}_{\text{NR}}{\cdot 1 00}\ [\%]. \tag{5}\]  
Finally, we calculate the actual modulation (ripple) of heart pulses in percentage (\(HP_{\text{RIPP}}\)) as  
\[HP_{\text{RIPP}}=(Lp_{\text{MAX}}-Lp_{\text{MIN}})/Lp_{\text{MAX}}{\cdot 1 00}\ [\%]. \tag{6}\]  
The determined \(Lp_{\text{MIN}}\), \(Lp_{\text{MAX}}\), \(L_{\text{OFS}}\) together with calculated \(PPG_{\text{RANGE}}\) and \(HP_{\text{RIPP}}\) values are visualized in Figure 4.  
The used methodology of heart rate values determined via PPG wave has been described in more detail in [30]. In principle, the procedure works in three basic steps: (1) systolic peaks are localized in the PPG signal, (2) heart pulse periods \(T_{\text{HP}}\) in samples are determined, (3) \(HR\) values are calculated using the sampling frequency \(f_{\text{s}}\) by a basic formula  
\[HR=60f_{\text{s}}/T_{\text{HP}}\ [\text{min}^{-1}]. \tag{7}\]  
The obtained sequence of HR values is next smoothed by a 3-point median filter and the linear trend (LT) is calculated by the mean square method. For LT \(<\) 0 the HR has a descending trend, for LT \(>\) 0 the HR values have an ascending trend. The resulting angle \(\varphi\) of LT in degrees is defined as \(HR\varphi_{\text{ LT}}=(\text{Arctg}(\text{LT})/\pi)\) 180. For the final stress evaluation rate determination in the fusion process, the relative parameter \(HR\varphi_{\text{ REL}}\) [%] for the \(q^{\text{th}}\) measurement phase is calculated in relation to the \(HR\varphi_{\text{ LT}}\) of the 1 st phase  
\[HR\varphi_{\text{ REL}}\ (q)=((HR\varphi_{\text{ LT}}(q)-HR\varphi_{\text{ LT}}(1))/HR\varphi_{\text{ LT}}(1)){\cdot 100}\ [\%]\ \text{ for }2\leq q\leq M. \tag{8}\]  
After the mean value \(HR_{\text{MEAN}}\) and LT removal of the smoothed HR sequence a relative variability \(HR_{\text{VAR}}\) based on the standard deviation \(HR_{\text{STD}}\) is calculated as  
\[HR_{\text{VAR}}=(HR_{\text{STD}}/HR_{\text{MEAN}}){\cdot 100}\ [\%]. \tag{9}\]For the purpose of this study, we use the ORI parameter which can also quantify the pain and/or stress in the human cardio-vascular system [6; 34]. The typical ORI range lies in the interval of <0.1, 0.3> for healthy people in a normal physiological state [10]. This parameter normalizes the width of the systolic pulse \(W_{\text{SP}}\) to the heart pulse period \(T_{\text{HP}}\)[35]  
\[ORI=W_{\text{SP}}/T_{\text{HP}}, \tag{10}\]  
where \(W_{\text{SP}}\) is determined typically at the height of two-thirds from the basis (one-third from the top--see Figure 5).