Сombined use of wavelets and sliding window for pulse signal processing under physical load

Abstract

The article presents a modern approach to pulse signal processing under conditions of physical exertion and in the recovery phase, which is based on the combined use of wavelet processing and the sliding window method. This approach allows overcoming the limitations of traditional time and frequency methods, providing a multi-scale time-frequency distribution of the signal and its precise temporal localization. Particular attention is paid to the use of the 4th-order Daubech wavelet (db4), which provides an optimal balance between sensitivity to sharp changes in the signal during exertion and smoothness in the recovery phase. Wavelet-energy analysis of the signal in the sliding window made it possible to track the dynamics of changes in the cardiovascular system, in particular: an increase in energy during exertion, reaching a peak value and a gradual return of the indicator to the baseline level in the recovery phase. The key indicator is the recovery time, which is defined as the interval between the moment of reaching peak activation and the return of the signal energy level to the resting state. To automate this process, an algorithm using a threshold device is proposed. At the first stage, a reference interval is selected before the start of the load, which characterizes the baseline wavelet energy at rest. Then, the threshold value is calculated according to the formula: Epor = 1.2 × Ebas, i.e. baseline energy plus 20% tolerance. This value allows you to take into account the variability of the signal and at the same time avoid false positives caused by noise or random fluctuations. The algorithm defines the recovery moment as the first time interval after physical exertion, in which the wavelet energy value steadily decreases and remains below the calculated threshold. This approach combines objectivity and accuracy, eliminating subjective errors in visual signal analysis. The practical significance of the developed method lies in the possibility of its application for assessing the fitness of athletes, controlling recovery processes in cardiology, monitoring the condition of patients in rehabilitation medicine, as well as in its implementation in portable fitness devices and telemetry systems. Thus, the combination of wavelet processing, window processing and the threshold recovery time algorithm creates a reliable tool for quantitatively assessing the adaptive capabilities of the cardiovascular system.