## 3 Method and Materials
### Biological Signal  
PPG Signal  
A pulse oximeter consists of a light emitter and a photodetector that collects and records (pulse or PPG signal) the loss--scattering and absorption--that a beam of light undergoes when it passes through, or is reflected by, a human tissue. It allows detecting blood volume changes in the microvascular bed of tissue--in our case, the middle finger of the left hand--, obtaining valuable information about the cardiovascular system and, on the whole, about the cardiorespiratory system [13]. Given the simplicity of its non-invasive accommodation, in addition to its low cost, a pulse oximeter is very useful in biomedical applications for clinical and sports environments [38]. For a good review, refer to the work of [PERSON] [39].  
In this work, we used forty PPG signals obtained from a national research study in 2015 [27; 28]. The project took data from 40 students between 18 and 30 years old and nonregular consumers of psychotropic substances, alcohol, or tobacco. The equipment used to measure all signals is the psychophysiological telemetric system \"Rehacor-T\" version \"Mini\" from Medicom MTD Ltd, measuring the PPG signal in the middle finger of the left-hand [27], with a sampling frequency of 250 Hz, say, with sampling time \(\Delta t=4\) ms.  
The main body of this paper shows the data of five subjects, illustrating the overall dynamic behavior of the 40 subjects who participated in the experiment (see Appendix A. Accompanying Material). The chosen PPG signals are represented in Figure 2. Depending on the analyzed factor, up to 600,000 points (40 min) were used, those corresponding to the total data recorded in the indicated research project. The results are consistent in the 40 subjects throughout the experimental measurement time of approximately 40 min for each one.  
The PPG signal is a complex signal composed of the peripheral pulse synchronized to each heartbeat (AC component of the PPG signal) and modulated by a quasi-DC component that varies slowly due to respiration, vasomotor activity, and vasoconstrtor waves [40]. As we will show later, the mutual coupling between the different components is intricate and operates at different timescales to regulate blood volume based on physiological needs [41; 42; 43; 44]. At small timescales, the regular cardiac rhythm quasi-periodically modulated by the breathing rhythm prevails [37; 45; 46], as reflected in the two prominent peaks  
Figure 2: (These pictures are made available for downloading in Supplementary Materials.) Each column corresponds with a subject (five individuals chosen randomly); the number of points: 30,000. (**a–e**) PPG signals, with amplitude normalized to the interval \([0,1]\)—for visual clarity, only 5000 points of each PPG signal are shown; (**f–j**) Power Spectrum Density (PSD). Two prominent peaks are clearly visible in each PSD, related to the respiratory (lower frequency peak) and heart (higher frequency peak) rates, whose values are indicated in bold text; (**k–o**) Representation of Equation (1) for \(c=2.5\), with \(N=5000\) points; (**p–t**) \(K_{m}\) results of the modified 0–1 test, for 100 random \(c\) values, with correlation method.  
in the PSD of a typical PPG signal, relating to the respiratory, lower frequency peak, and heart, higher frequency peak, rates (see Figure 2f-j).