Application of Taylor–Fourier Analysis to Photoplethysmography Signals for Instantaneous Heart Rate Measurement

Photoplethysmography (PPG) is gaining increasing attention for the measurement of heart rate (HR) and HR variability (HRV), but the accuracy and reliability of measurement results remain questionable when obtained from wearable devices, prone to recording movement artifacts and other disturbances caused by poor sensor-skin contact. HR and HRV information is typically extracted in the time domain, from the estimation of interbeat intervals (IBIs), which can be confidently identified only when the signal is very clean. This article proposes an alternative time–frequency approach to HR estimation, based on the Taylor-Fourier (TF) analysis, which allows obtaining the instantaneous HR, as opposed to the traditional beat-to-beat average HR, with associated benefits in terms of time resolution (especially for HRV measurements), no quantization, and enhanced robustness in the presence of moderate signal distortion. Experimental tests on a healthy subject wearing the Empatica E4 wristband have been complemented by additional validation on a dataset of recordings from 18 healthy subjects, using the same device; in all cases, the results from the proposed method have been compared to HR measurements from electrocardiography (ECG), with very good agreement. The results have also been compared to the closest alternatives for instantaneous HR estimation, relying on the short-time Fourier transform (STFT), or on the empirical mode decomposition (EMD) combined with the Hilbert transform (HT), confirming the noticeable benefits provided by the proposed model-based approach, particularly evident in its ability to better reveal the high-frequency HR oscillations, mainly caused by respiration.