Modelling and filtering almost periodic signals by time-varying Fourier series with application to near-infrared spectroscopy

We propose a new approach to modelling almost periodic signals and to model-based estimation of such signals from noisy observations. The signal model is based on Fourier series where both the coefficients and the fundamental frequency can continuously change over time. This signal model can be represented by a factor graph which we use to derive message passing algorithms to estimate the time-dependent model parameters from the observed samples. Our motivating application is near-infrared spectroscopy. In this application the observed signal is a superposition of several physiological signals of clinical interest (including, in particular, the arterial pulsation), and we wish to decompose the observed signal into these components. Most of these component signals are almost periodic. We show that the proposed algorithm can be used to extract the arterial pulsation from the measured signal.