# Online Algorithm for Deriving Heart Rate Variability Components and Their Time-Frequency Analysis
## 5 Conclusions  
This study presents and validates two new HRV signal decomposition methods, VMDon and AVMD, compared to the algorithms previously used for this purpose. To the best of the authors' knowledge, the online algorithm decomposing HRV into HF, LF, VLF, and VLF waveforms has been proposed for the first time. The results of the work also indicate which decomposition approaches are the best, in particular which method (including new and previously used ones) is the most precise for a given component: AVMD is the more accurate for HF and LF components extraction and VMDon for VLF and ULF ones, the latter of which can also be used offline in this form. Furthermore, the suitability of CWT for VFL component derivation is also demonstrated. In particular, they can be applied to the same data, allowing for the accurate extraction of all four HRV components. HRV decomposition results from 36 subjects suggest slightly different frequency ranges of the components than those usually proposed in the literature and the possibility of mixing their modes, which should be considered in the future work on this topic. Consistent results in this respect were obtained using the three best decomposition methods, which confirm the reliability of the component characteristics assessed in this work. Now, for the convenience of use in the future work, they are gathered together in Table 4.  
There are still a few other aspects to work on. First, one can try to develop a comprehensive online algorithm to extract HRV components directly from ECG signal, possibly to be embedded in, e.g., Holter devices. Having isolated HRV components, it will be easier to identify the relationship of low-frequency waveforms (VLF, ULF) with specific physiological processes through ECG/HRV analysis for cases when other biosignals were recorded at the same time. In addition, the correct extraction of HRV components also creates a new possibility to infer sinus rhythm stimulation by attempting to invert the integral pulse frequency modulation (IPFM) models. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15031210/s1](https://www.mdpi.com/article/10.3390/app15031210/s1)]([https://www.mdpi.com/article/10.3390/app15031210/s1](https://www.mdpi.com/article/10.3390/app15031210/s1)), Table S1: [PERSON]'s correlation \(r_{s}\) between results of VMDon and AVMD for real HRVs from St. Vincent University Hospital database; Table S2: [PERSON]'s correlation \(r_{s}\) between results of VMDon and AVMD for real HRVs from Apnea-ECG database; Table S3: [PERSON]'s correlation \(r_{s}\) between results of VMDon and CWT for real HRVs from St. Vincent University Hospital database; Table S4: [PERSON]'s correlation \(r_{s}\) between results of VMDon and CWT for real HRVs from Apnea-ECG database; Table S5: The AM and FM ranges in the population of 18 subjects from St. Vincent University Hospital database; Table S6: The AM and FM ranges in the population of 18 subjects from Apnea-ECG database; Table S7: The AM and FM ranges in the population of 36 subjects from combined databases. Conceptualization, K.A. and A.G.P. ; methodology, K.A. and A.G.P. ; software, K.A. ; validation, K.A. and A.G.P. ; formal analysis, K.A. and A.G.P. ; investigation, K.A. ; resources, K.A. ; data curation, K.A. ; writing--original draft preparation, K.A. ; writing--review and editing, \begin{table}
\begin{tabular}{l l l} \hline \hline
**Component** & **AM (ms)** & **FM (mHz)** \\ \hline HF & 1.1–202 & 111–398 \\ LF & 2.5–169 & 29–137 \\ VLF & 7.7–162 & 4.7–31 \\ ULF & 7.7–175 & 0.002–3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The AM and FM ranges (99 th percentile) in the population of 36 subjects. A.G.P. ; visualization, K.A. ; supervision, A.G.P. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.