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One of the most challenging applications of time-frequency representations deals with the analysis of the signal issued from natural environment. Recently, the interest for passive underwater context increased, basically due to the rich information carried out by the natural signals. Taken into account the non-linear multi-component time-frequency behavior of such signals, their analysis is a complex problem. In this paper we introduce a new time-frequency analysis concept that aims to extract the non-linear time-frequency components. The main feature of this technique is the joint use of time-amplitude, time-frequency and time-phase information. This is materialized by a short-time polynomial phase modeling and the fusion of local information according to the best locally matches of local cubic frequency modulations. Tests provided on real data illustrate the benefits of the proposed approach.