## 2 Materials and Methods  
### Biological Data  
Health monitoring by non-invasive means has attracted the attention of medical specialists for some years now since it allows advancing preliminary diagnoses on possible pathological dysfunctions, whether chronic or transient. Some scientific evidence sustains the relationship between the biological signals generated by the human body and the health status of the individual, as skin temperature (ST), electrodermal activity (EDA), pulse wave or photoplethysmography (PPG), electrocardiography (ECG), electromyography (EMG), respiration (Resp. ), pupil diameter (PD), electroencephalography (EEG), and blood pressure, among others. The information provided by all these biological signals depends on the knowledge available about the underlying physiological processes. The study of the dynamics of all these biological signals will help to understand better the physiological system that generates them. Furthermore, it would help to get an insight into how different dynamic variables couple, as, for instance, the heart and respiratory frequencies, in order to keep the physiological system in a perfect condition, preventing its deterioration towards a pathological state. In this paper, we focus only on a single biological signal, the PPG signal; future publications will describe the results for more biological signals. We chose the PPG signal because it is easily accessible. 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 [16]. 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. 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 [17] and sports environments [18]. As with other biological signals, characteristics extracted from the PPG signal allow to no small extent identifying ideal health conditions and their possible deviations. Thus, indicators associated with different pathologies could be established, which anticipate their severity according to the causes that gave rise them. Typically, these indicators in the case of PPG signal were based on the morphology of the signal rather than on its dynamics [17; 19]; we think that by studying dynamic aspects of the PPG signal, the physiological system that generates it can be better understood. With the aim of examining the PPG signal dynamics, we used the PPG signals (to show in this paper only five individuals chosen randomly) from a total of 40 students, between 18 and 30 years old, and non-regular consumers of psychotropic substances, alcohol, or tobacco, selected to participate in a  
Figure 2: From a sequence of scalar measurements: (**a**) data and requirements; and (**b**) the reconstruction done in this paper for the PPG signal following the lag or delay method. The description of the concepts is in Section 2.2, and the application results are in Section 3.  
national research study [20; 21]; the five PPG signals shown in this paper were the same as those used in previous research that confirmed the predominantly quasi-periodic behavior for small timescales in healthy young people with a modified version of the 0-1 test [22]. Showing more than five subjects will not clarify the proposed method. The results would be similar. Remember that the fundamental frequency of the PPG signal is typically around 1 Hz, depending on the heart rate (0.5-4 Hz, first and second harmonic) and respiratory activity at roughly 0.2-0.35 Hz. We applied a Butterworth bandpass filter with cutoff frequencies at 0.01 and 8 Hz, in order to avoid high-frequency noise and, to some extent, motion artifacts [23].