Online Algorithm for Deriving Heart Rate Variability Components and Their Time–Frequency Analysis

Featured Application: This work makes possible to extract heart rate variability components online in order to monitor the underlying human body systems, in particular to determine the activity of the sympathetic and parasympathetic branches of the autonomic nervous system (ANS) as well as the balance between them, and indirectly in detecting and monitoring many common diseases related to the cardiovascular system and ANS. Such a solution can, for example, be directly embedded into Holter devices. A more precise determination of the components’ properties can give the opportunity to link them to specific physiological processes, especially those of very low and ultra-low frequencies, which has not yet been fully achieved, increasing the practical importance of this research. Heart rate variability (HRV) containing four components of high (HF), low (LF), very low (VLF), and ultra-low (ULF) frequencies provides insight into the cardiovascular and autonomic nervous system functions. Classical spectral analysis is most often used in research on HRV and its components. The aim of this work was to develop and validate an online HRV decomposition algorithm for monitoring the associated physiological processes. The online algorithm was developed based on variational mode decomposition (VMD), validated on synthetic HRV with known properties and compared with its offline adaptive version AVMD, standard VMD, continuous wavelet transform (CWT), and wavelet package decomposition (WPD). Finally, it was used to decompose 36 real all-night HRVs from two datasets to analyze the properties of the four extracted components using the Hilbert transform. The statistical tests confirmed that the online VMD (VMDon) algorithm returned results of comparable quality to AVMD and CWT, and outperformed standard VMD and WPD. VMDon, AVMD, and CWT extracted four components from the real HRV with frequency content slightly exceeding the previously recognized ranges, suggesting the possibility of their modes mixing. Their ranges of variability were assessed as follows: HF: 0.11–0.40 Hz; LF: 0.029–0.14 Hz; VLF: 4.7–31 mHz; and ULF: 0.002–3.0 mHz. © 2025 by the authors.