## 2 Methods
### Signals Classification  
The next step after database selection was to find relevant signal morphology characteristics among different patient groups as was described earlier. The main observations during recordings evaluation in different scenarios, while also having in mind the findings reported in the medical literature [18; 19; 20; 21; 22] were:  
* An narcotic limb features are found in many cases in the old patients group or for hypertensive ones. They represent a change in signal slope, PPG, or BP, during the systolic rising phase. * Dicrotic wave location moves away with respect to SYS points when vasodilators were administrated during the beginning of anesthesia. The vasoconstrtictor drugs give the opposite effect by moving the dicrotic wave toward SYS peak. Therefore, this fiducial point can represent the state of vasomotor activity. * Dicrotic wave is mostly absent in the children group, under 10 years old, and very prominent in young groups with ages between 20 and 30. After these limits, in older populations it fades again. Another observation, but related to signal acquisition, is the different protocols used for PPG recordings. One important highlight used sampling frequency but also the cutoff frequency for signal filtering. This variation is translated into different cardiovascular details which will be discussed in the Results and Limitations sections. Those differences among databases did not represent a blocking point for the current step but could influence the performance of the final algorithm. After the signal characteristics arise, we needed a tool to translate it into a numerical value. A good domain to highlight signal morphology was first derivative (FD) since it represents the evolution of the signal gradient over time. This domain has the advantage to show a more detailed level of the investigated waveforms which are not visible by the eye. Therefore, after the initial pre-evaluation steps, we define four major classes among patients without cardiovascular disease which modulated PPG or BP signals such as pulsus bisefience. The defined classes take the dicrotic wave and an narctic feature as the selection criteria:  
* An narcotic type (A)--This class highlights the pre-systolic phase where signal slope is subject to a change [18; 19]. This feature is translated into FD domain as a visible peak before SYS maximum point event as it is shown in Figure 3a. * Normal type (N)--This class highlights the post-systolic phase where DCW generates a visible peak in the original analyzed signal. In FD domain, the associated gradient of the dicrotic wave beginning phase is greater than zero (or positive), building a peak as shown in Figure 3b. * Collapsing type (C)--Also aims at the post-systolic phase where DCW is entirely absent in the analyzed signal. In FD domain its gradient does not appear as the result of a wave missing. After the SYS event, the returning gradient slowly rises towards zero axis, without generating a peak, until the next cardiac cycle begins [20] as shown in Figure 3c. * Normal Collapsing (NC) type--This class is a characterization between the previous two. DCW is barely visible in the investigated signal, therefore, it generates a gradient peak into FD domain but negative in absolute value as shown in Figure 3d. Note that multiple peaks after SYS event can occur due to different elastic characteristic of the arterial network. These peaks can be present even if the signal filtering is applied and are therefore not given by motion or acquisition artifacts. In our classification context,  
Figure 3: PPG signal morphology classification by DCW behaviour in FD domain in healthy patients, also applicable for BP signal. Discussion in the text. Red lines represent the correspondence between original signal and its gradient peak location in FD; the associated amplitude is marked with green arrow; exception for anacrotic case where the gradient is marked with red circle.