A stochastic sinusoidal model with application to speech and EEG-sleep spindle signals

In this paper, we propose to investigate stochastic sinusoidal models in order to characterise quasi-periodic signals. Indeed, in comparison to the broadly used autoregressive (AR) models, a sinusoidal approach seems to be more efficient to capture quasi-periodic feature. Using AR process as a model for the sine wave magnitudes makes it possible to track the frequential non-stationarity of the signal. The scheme we propose operates as follows: once the frequency components of the signal are obtained, estimating the magnitudes of each sine component of the model is performed by means of an Expectation-Maximisation (EM) algorithm based on Kalman smoothing. Results are provided on sleep spindle and speech.