Estimating the period and the shape of a periodic component in short duration signals

Estimating the period and the shape of a periodic component in a short duration signal at the output of a sensor is often of great importance in many applications and in particular in biological data. Classically Fourier Transform (FT) methods are used for this task, but they lack precision and resolution when the duration of the signal is as short as two periods. In this paper, we present a new nonparametric method which is able to estimate the period very precisely and to estimate the shape of the periodic component. The method is based on the direct description of the problem as a linear inverse problem and a Bayesian inference approach. The main idea is to write down the expression of the joint posterior law of the period and the shape of the periodic component given the noisy data and a prior smoothness model on the shape. Then, using this posterior law we can determine both the period and the shape of the periodic component. Some results on synthetic data show the performance of the proposed method.Estimating the period and the shape of a periodic component in a short duration signal at the output of a sensor is often of great importance in many applications and in particular in biological data. Classically Fourier Transform (FT) methods are used for this task, but they lack precision and resolution when the duration of the signal is as short as two periods. In this paper, we present a new nonparametric method which is able to estimate the period very precisely and to estimate the shape of the periodic component. The method is based on the direct description of the problem as a linear inverse problem and a Bayesian inference approach. The main idea is to write down the expression of the joint posterior law of the period and the shape of the periodic component given the noisy data and a prior smoothness model on the shape. Then, using this posterior law we can determine both the period and the shape of the periodic component. Some results on synthetic data show the performance of the proposed method.