## 2 Methods
### Signals Classification
Black lines represent the correspondence between the original signal and its zero crossing location marked with red cross. the dicrotic wave presence is flagged as the strongest gradient in FD domain in the defined search window. Using this major classification, signals are characterized from a qualitative mean with an intuitive nomenclature. In order to cover a quantitative topic, a numerical term should be associated to gradients since it can range from any positive to negative value. As we anchor classification to the dicrotic wave gradient it needs to be related to another important key metric during the current cardiac cycle. Thus, a numerical parameter was defined, labelled as DtS which stands for Dicrotic to Systolic Ratio. The computed parameter translates into numbers of the human's sense of the observed PPG morphologies during signal evaluation step. In this way, it is characterized how strong the dicrotic wave is with respect to the systolic one according to the presented classifications from Figure 3. The formula for defining this morphological parameter is:  
\[\text{DtS}=\frac{\text{g}_{\text{SYS}}-\text{g}_{\text{DCW}}}{\text{g}_{ \text{SYS}}}\]  
where gSYS represents the value of systolic gradient extracted from the first derivative and gDCW is the value of the dicrotic gradient part. While the SYS gradient is always positive, the other ones take both possibilities. This is why the DtS parameters compute the distance between the gradients of the respective fiducial points with respect to the positive ones. With this rule, the translation of defined classes was translated via DtS parameters as presented in Table 2.  
Note that DtS is computed per individual cardiac cycle. Thus, in N type signal where gDCW is defined to be positive, the above parameter will be lower than 1 value. While in NC type were DCW gradient is negative, the parameter will be greater than 1. In other words, DtS highlights how close the dicrotic wave gradient is to the systolic one in the FD domain. For C type where dicrotic is entirely absent, DtS cannot be computed but is marked with value 2. This convention comes from the fact that a hypothetically maximum negative value taken by a second wave cannot exceed absolute value of the current systolic gradient. As we described earlier, a strong FD value represents a strong visible point back to the analyzed signal. If a signal recording is evaluated during multiple periods, the above-described parameters is computed as a mean. With those classifications--nomenclature of waveform morphology by pre-systolic and post-systolic evaluation criteria--we built a test labelled ANC Test(tm (**A**nacrotic, **N**ormal, **C**ollapsing) which stands for Level 1 class prediction described back in Figure 1. Hence, the numerical outputs of this designed test, which are intended for multiple cardiac cycles evaluation, are:  
* Anacrotic occurrence if at least two cardiac cycles are evaluated within the pre-systolic phase. For a single-period analysis, the algorithm just marks if the Anacrotic feature is present or not. * Normal, Normal-Collapsing and Collapsing occurrence evaluated in the same manner as above but within the post-systolic phase. * DtS ratio evaluation for every individual analyzed cardiac cycle. In the collapsing case the ratio is marked with code 2 since mathematically it cannot be computed. All the occurrence computations are done automatically since one part of the intended algorithm classified recordings by the defined features. In multiple periods of evaluation \begin{table}
\begin{tabular}{c c c c} \hline
**Class** & **gSYS** & **gDCW Value Interval** & **DtS Value Interval** \\ \hline N & & (0:gSYS) & (0:1) \\ \hline NC & Always \textgreater{}0 & (\(-\)gSYS:0) & [1:2) \\ \hline C & & N/A & 2 * \\ \hline \end{tabular}  
* It’s a convention code since DtS doesn’t have this computed value assigned.  
\end{table} 
Table 2: Numerically values associated with defined classifications. mode, the occurrence rate for the presented types can takes any value between 0% and 100%.