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A new digital signal-processing method for instantaneous frequency estimation is here proposed. The attention is mainly paid to signals whose instantaneous frequency trajectories exhibit a periodic evolution versus time. Thanks to an optimized use of the warblet transform, the method assures superior accuracy and resolving capability with respect to other solutions already available in the literature, thus showing itself very attractive in the presence of multicomponent signals characterized by instantaneous frequency trajectories extremely similar and very close to one another. Theoretical notes regarding the warblet transform and its optimized use in the framework of the proposed method are first given. Then, the fundamental steps of the method are described in detail with references to a clarifying example. The results of a number of experiments on emulated and actual signals, aimed at assessing the performance of the method, are finally presented.