Weighted Iterative Complex Demodulation for High-Resolution Instantaneous Frequencies in Low-Frequency PPG Signals From Wearable Devices

In this study, we present the development and validation of an advanced signal processing algorithm, weighted iterative time-frequency complex demodulation (wi-TFCD), designed to enhance noise suppression and improve time-frequency resolution in low-frequency physiological signals. We evaluate wi-TFCD against traditional methods such as short-time Fourier transform (STFT), variable frequency complex demodulation (VFCDM), and the baseline iterative TFCD (i-TFCD), using both synthetic chirp signals contaminated with additive Gaussian white noise and real-world photoplethysmography (PPG) signals recorded during exercise. The results demonstrate that wi-TFCD consistently outperforms the other methods, achieving the lowest Rényi entropy and the highest Stanković concentration, which correspond to improved spectral compactness and clarity. For a sinusoidal chirp signal, wi-TFCD achieves a Rényi entropy that is 1.29 times lower than VFCDM and 1.27 times lower than i-TFCD, a Stanković concentration 3.62 times higher than VFCDM and 3.01 times higher than i-TFCD, and a mean square error (MSE) that is 1.29 times lower than VFCDM and 1.11 times lower than i-TFCD, demonstrating superior resolution and robustness under noise. In PPG-based heart rate (HR) estimation across 55 subjects, wi-TFCD achieves a mean absolute error (MAE) of 4.99 bpm, compared to 5.19 bpm for i-TFCD and 5.42 bpm for VFCDM. These findings confirm that wi-TFCD provides more precise signal representation and robust physiological monitoring, making it a promising tool for wearable health applications where motion artifacts and noise are prevalent.