Modeling of long-time multicomponent signals with nonlinear frequency and amplitude modulations : component tracking in the time-frequency plane
In this thesis, a novel method is proposed for modeling the non-linear amplitude and frequency modulations of non-stationary multi-component signals of long duration. The method relies on the decomposition of the signal into short time segments to carry out local modelings on these segments. In order to initialize the modeling, a first step is designed which can be considered as an independent estimator of the modulations over the entire duration of the signal. The originality of this approach lies in the definition of the total divergence matrix integrating simultaneously the amplitude and frequency values, which are employed for the association of a peak to a component according to a stochastic acceptation criteria. Following the initialization, the proposed method estimates the modulations by the step sequence of segmentation, modeling and fusion. The locally obtained modulation functions estimated by maximum likelihood are finally connected in the fusion step which suppresses their discontinuity and yields the global estimation over the entire signal duration. All these steps are defined in order to be able to model multicomponent signals with births and deaths, making one of its original features compared to existing techniques. The results on real and simulated signals have shown the good performance and adaptability of the proposed method.