## 2 Methods
### Wavelet Analysis and the Cone of Influence  
For WA, selecting an appropriate set of basic functions is crucial, as it determines the time-frequency localization of the decomposed signal and should align with the application requirements. A family of wavelet functions \(\psi_{\tau,s}\), generated from a mother wavelet \(\psi(t)\), is defined as Equation (1) [17]:  
\[\psi_{\tau,s}\ =\ \frac{1}{\sqrt{s}}\ \psi\left(\frac{t-\tau}{s}\right) \tag{1}\]  
with the parameter \(s\) representing the scale that stretches and compresses the wavelet and the parameter \(\tau\) representing the time-translation parameter. In our work, Morlet's set of basic functions were used [4; 7]. It is composed of shifted and scaled versions of [PERSON]'s mother wavelet \(\psi(t)_{Morlet}\) consisting of a complex exponential carrier with a center frequency of \(f_{0}\) multiplied by the Gaussian envelope, as shown in Equation (2) [17]:  
\[\psi(t)_{Morlet}=\frac{1}{\pi^{-1/4}}e^{2i\pi f_{0}t}e^{\frac{-i^{2}}{2}} \tag{2}\]  
While the latter provides good localization in time, the oscillatory sinusoidal component provides frequency content by allowing the wavelet to align with oscillations that constitute a signal. As a result, the Morlet wavelet can effectively capture both transient and oscillatory components at specific frequencies, providing a good balance between both time and frequency localization of the inspected LD signal. Furthermore, as Morlet's wavelets are scalable, variable time-frequency resolution of the reconstructed signal is provided. This property is essential for our work as it provides reliable detection of both high and low-frequency LD signal content. In this work, WA was calculated using a custom-written MATLAB algorithm. We implemented a continuous WT (cwt), which provides a two-dimensional representation of the reconstructed signal in terms of time and frequency (scalograms depicted in Figure 1B,C). While cwt is mathematically defined by Equation (3) [17],  
\[F(\tau,s)\ =\ \frac{1}{\sqrt{s}}\int_{-\infty}^{\infty}f(t)\psi^{*}\left( \frac{t-\tau}{s}\right)\text{dt} \tag{3}\]it is in practice computed numerically using MATLAB's cwt function, which discretizes time scales and steps, as shown in Equation (4) [18]:  
\[F(\tau,s)\ =\ \frac{1}{\sqrt{s}}\sum_{m\ =\ 0}^{N-1}f[n]\ \psi^{*}\bigg{(}\frac{n \Delta t-\tau}{s}\bigg{)}\Delta t \tag{4}\]  
In Equation (4), \(f[n]\) represents the discrete samples of the input LD signal, \(N\) the total number of discrete samples, and \(\Delta t\) the sampling interval of the signal (inverse of the sampling frequency). Scales were spaced logarithmically to ensure adequate resolution across all frequency bands while maintaining computational efficiency, with MATLAB handling this internally. To quantify the contribution of the characteristic frequency intervals related to physiological influences, we further decomposed the LD signals into their characteristic time-averaged wavelet power spectra, which were obtained by averaging the wavelet scalograms over time. The time-averaged spectra were constructed in two ways: without and with excluding the data covered by the COI (Figures 1 and 2). We used an approximation to the \(1/e^{2}\) rule to delineate the COI [5], a method that is integrated in MATLAB. The absolute median power within each frequency interval of interest and the absolute median power of the entire power spectrum were calculated for each individual in the corresponding phase. Finally, the relative power (RP) was calculated as the ratio between the absolute median power within the frequency interval of interest and the absolute median power of the whole spectrum. Figure 1: _Cont._  
Figure 1: A representative tracing of the raw laser Doppler fluxmetry (LDF) signal of skin microcirculation obtained at the solar forearm during the baseline, occlusion, and the post-occlusive reactive hyperemia (PORH) (**A**).