## 2 Materials and Methods
### Description of Variables and Signal Processing  
Filtering and artifact removal were performed using Butterworth bandpass filters for both ECG and PPG signals. Specifically, these signals were filtered within the frequency ranges of 0.1-50 Hz and 0.1-5 Hz, respectively. After filtering, the signals were corrected for in the baseline to eliminate the DC component using the ModPoly [29] method from the BaselineRemoval library. Finally, for both raw and extracted variables, a threshold-based random peak removal technique was employed. This method removes atypical clusters of points within a defined interval on the magnitude axis, based on a set threshold. Subsequently, three subsignals and a principal value were derived from the ECG and PPG signals. These three temporal series are illustrated in Figure 1, and are as follows: heart rate variability (HRV), respiration signal (RES), and pulse transit time (PTT), with heart rate (HR) being the predominant measurement. For HRV, the intervals corresponding to each R peak of the ECG signal were determined, thus generating a time vector. This vector was then utilized to generate the HRV signal by subtracting from a version of itself shifted one position to the right, thus containing the intervals between consecutive R peaks. In determining the respiration signal, we used the ECG-derived respiration method (EDR). This technique facilitates the approximation of the respiration signal by filtering the ECG signal within a frequency range encompassing the respiratory components (0.13-0.35 Hz). The R peaks of the ECG are subsequently identified and interpolated using a cubic spline to derive the respiration signal from the ECG. Lastly, the PTT signal was obtained, which reflects the duration of propagation of a heartbeat from the heart to the most distal part of the hand. This was achieved by aligning the time instances of the maximal peaks in the PPG signal with the time vector derived from the R peak of the ECG signal and subtracting the latter. Thus, a distinct time vector was formulated, representing the PTT signal. The heart rate was ultimately determined by counting the number of R peaks in the ECG over a one-minute duration and dividing this by 60 s.  
The variables used in this analysis are delineated as follows. From the outset, the concept of physiological coherence, as elucidated by the HeartMath Institute in numerous research studies, was considered crucial. This notion describes the degree of synchronization or equilibrium among disparate oscillatory systems, proposing that when one system achieves a state of coherence and subsequently interacts with another, it can produce a comparable state of equilibrium in the latter, thus augmenting its functional efficiency [30]. Figure 1: This figure shows a brief visual explanation of how the subsignals are obtained for: (**1**) heart rate variability, (**2**) ECG-derived respiration obtained by interpolation, and (**3**) pulse time transit by PPG and ECG interaction. Consequently, this metric has been shown to reflect relative variations in various emotional states. Initially, physiological coherence was intended to be assessed by heart rate variability (HRV), as stated in (1):  
\[\text{PhyCoh}=\frac{P_{\text{Peak}}}{(P_{\text{Total}}-P_{\text{Peak}})^{2}} \tag{1}\]  
where \(P_{\text{Peak}}\) is known as peak power, and is related to the power of the highest peak within a lower frequency band (designated between 0.04 and 0.5 Hz) of the power spectrum of an HRV signal, specifically within 0.04 and 0.26 Hz. Furthermore, \(P_{\text{Total}}\) is the total power of the specified lower frequency band [30]. Physical coherence is a number between 0 and 1. To achieve this, (1) is modified and the resulting equation is shown in (2). This modification was necessary due to an error in the original (1) that could cause the coherence number to exceed 1 [31].