A Frequency Estimation Scheme Based on Gaussian Average Filtering Decomposition and Hilbert Transform: With Estimation of Respiratory Rate as an Example

Frequency estimation plays a critical role in vital sign monitoring. Methods based on Fourier transform and eigen-analysis are commonly adopted techniques for frequency estimation. Because of the nonstationary and time-varying characteristics of physiological processes, time-frequency analysis (TFA) is a feasible way to perform biomedical signal analysis. Among miscellaneous approaches, Hilbert–Huang transform (HHT) has been demonstrated to be a potential tool in biomedical applications. However, the problems of mode mixing, unnecessary redundant decomposition and boundary effect are the common deficits that occur during the procedure of empirical mode decomposition (EMD) or ensemble empirical mode decomposition (EEMD). The Gaussian average filtering decomposition (GAFD) technique has been shown to be appropriate in several biomedical scenarios and can be an alternative to EMD and EEMD. This research proposes the combination of GAFD and Hilbert transform that is termed the Hilbert–Gauss transform (HGT) to overcome the conventional drawbacks of HHT in TFA and frequency estimation. This new method is verified to be effective for the estimation of respiratory rate (RR) in finger photoplethysmography (PPG), wrist PPG and seismocardiogram (SCG). Compared with the ground truth values, the estimated RRs are evaluated to be of excellent reliability by intraclass correlation coefficient (ICC) and to be of high agreement by Bland–Altman analysis.