# Portable Sensor System for Registration, Processing and Mathematical Analysis of PPG Signals
## 1 Introduction  
The prevention of cardiovascular diseases and their early detection is one of the main areas of modern cardiology [1; 2]. Usually, studies in hospitals and clinics are done after the disease has already occurred. One way to prevent and reduce the risk of cardiovascular disease is to use portable devices designed to detect changes in blood volume in the blood vessels based on the photoplethysmographicmethod. The non-invasive photoplethysmographic (PPG) method is an effective way to study heart rate and cardiovascular disease, monitor respiratory rate, blood oxygen saturation, autonomic functions, and tissue perfusion [3]. Through the PPG method, assessments can be made of the aging processes of the vascular system, the monitoring of hypertension, atherosclerosis, early screening, and assessment of arterial stiffness and elasticity [4]. Portable PPG devices must work reliably under the conditions of free movement activity and allow them to be used for a long time. The amount and quality of diagnostic information obtained with these devices must be sufficient to form a conclusion regarding the condition of the cardiovascular system and its modification. PPG-based medical systems should be cheap and easy to use, enable reliable processing of retrieved biomedical signals, and the rapid transfer of processed data and the results of mathematical analysis. The portable PPG devices used in the diagnosis of cardiovascular disease are among the most sought after medical devices. These devices are an alternative to electrocardiographic (ECG) devices and they are used in several applications, such as modern, non-invasive, convenient, and inexpensive equipment. The assessment of the physiological parameters of the human body based on photoplethysmographic signals that were recorded by portable PPG devices is an up-to-date scientific task. Applying innovations in this area will lead to the widespread use of these types of devices to reduce cardiovascular mortality. According to a study [5; 6], the use of the parameters that were determined in the mathematical analysis of PPG data for the diagnosis and prevention of cardiovascular disease is an unresolved problem. As is well known, PPG and electrocardiographic (ECG) signals today are regarded as nonlinear and non-stationary processes that have periodic and chaotic components. At the end of the 20 th century, based on the ideas of the Nobel laureate [PERSON], [PERSON] suggested that the heart be considered as an open, non-linear, and nonequilibrium system [7]. He identifies it as the first major task facing scientists, physiologists, and physicians, the pooling of their efforts, and knowledge in the search for new ways to solve a number of clinical problems, thus to help a large number of patients with cardiovascular diseases. The existing nonlinearities in the heart's regulating systems determine the chaotic nature of the heart rhythm, with each PP (RR) interval (PP and RR are the intervals between successive heartbeats) different from the rest, as they are unique [8]. The reason for the appearance of randomness in the photoplethysmograms (electrocardiograms) is related to the randomness of the processes that takes place in the heart. Therefore, it is appropriate to use nonlinear dynamics methods, such as fractal and multifractal methods for evaluating the information characteristics of the internal organization of PPG signals [9]. Processes with fractal characteristics have the following properties: fractal dimension and self-similarity. The fractal dimension (D) is determined by the following formula: \(\mathrm{D}=2-\mathrm{H}\), where \(\mathrm{H}\) is a Hurst exponent [10]. The formula shows that the Hurst exponent is one of the key indicators characterizing fractal signals. In the physical sense, this parameter characterizes the degree of self-similarity, as well as the complexity of the dynamics and the correlation function of the investigated signal.