Direct nonparametric estimation of the period and the shape of a periodic component in short duration signals

In this paper a new direct nonparametric estimation of the period and the shape of a periodic component in short duration signals is proposed and evaluated. Classical Fourier Transform (FT) methods lack precision and resolution when the duration of the signal is very short and the signal is noisy. The proposed method is based on the direct description of the problem as a linear inverse problem and a Bayesian inference approach with appropriate prior distributions. The expression of the joint posterior law of the period and the shape of the periodic component is obtained and used to determine both the period and the shape of the periodic component. Some results on synthetic data show the performance of the proposed method compared to the state of the art methods.