Adaptive modelling and filtering of periodic signals with non-stationary fundamental frequency

We present a novel approach to processing periodic signals with non-stationary fundamental frequency. These quasi-periodic signals feature a perpetually recurring underlying signal pattern and arise in various fields of science and engineering. The proposed method integrates a recursive extraction of the signal pattern with dynamic tracking of the instantaneous phase to effectively suppress measurement noise without prior knowledge of the signal characteristics or the frequency variation. The performance is showcased both in simulation and using experimental measurements of the cardiac cycle obtained by a nitrogen-vacancy diamond quantum sensor. Overall, high-fidelity signal reconstruction and convincing pattern learning is achieved, even in the presence of complex non-linear disturbances and non-Gaussian noise. Conclusively, the proposed technique constitutes a flexible and efficient solution, addressing limitations of existing methods and offering real-world applicability.