# Online Algorithm for Deriving Heart Rate Variability Components and Their Time-Frequency Analysis
###### Abstract
Empirical mode decomposition (EMD), on the other hand, is a method designed to extract oscillating components from nonlinear and non-stationary signals [35] and is often followed by the Hilbert transform (HT) to derive instantaneous amplitudes and frequencies [4; 23; 29; 34; 36; 37]. Multiband filtering (MBF) is an old and seldom used method nowadays, requiring the knowledge of frequency bands for filtering [38], but a recent study has shown that it can give comparable or better results than STFT or EMD [39]. Spectral filtering effects can also be obtained using the wavelet transform, which is a relatively new tool for analyzing non-stationary signals. This is achieved due to the local time properties of the analyzing wavelets and the well-defined frequency properties of the components obtained by the inverse transform. The wavelet transform (WT) was recently used to decompose HRV into three variants: continuous (CWT), discrete (DWT), and wavelet package decomposition (WPD) [40; 41; 42; 43]. One of the newest methods for nonlinear analysis of non-stationary signals is variational mode decomposition (VMD), splitting a signal into several intrinsic mode functions (IMFs), similarly to EMD [44]. While the original VMD procedure requires specifying the number of searched IMFs [45; 46], which is a disadvantage compared to EMD, recently an adaptive and data-driven version of this algorithm (AVMD) has been proposed that automatically determines the optimal value of the IMFs [47]. This solution was tested on overnight HRV signals and was able to successfully extract all four components in the offline analysis, outperforming MBF, STFT, and EMD. In summary, the existing current algorithms operate offline for the vast majority of time, which does not allow for monitoring changes in the frequency components continuously. Meanwhile, the courses of individual components indicate the current processes in various systems of the human body. In addition, older decomposition methods are used (like STFT, EMD, WT, or classic VMD), and VLF and ULF are mostly ignored, still leaving many questions about their nature unanswered. Moreover, there is still a large uncertainty as to the instantaneous properties of the VLF and ULF waveforms, which prevents further research on their internal connections with the physiological processes of various body systems. The solution to these problems would be to develop an algorithm allowing for the online HRV decomposition and thus the monitoring of the underlying processes. The aim of this work was to develop and validate an online HRV decomposition algorithm yielding simultaneously all four frequency components and to use it to analyze the real HRV signals in a continuous mode. By design, this algorithm should not impose sharp boundaries on the frequency content of the components, and thus, the obtained results can be used to more precisely determine their amplitude-frequency variability. In the following sections, the data used and the methodology applied are explained, and the results obtained are presented and discussed. Finally, the main conclusion regarding the suitability of the proposed method is provided.