In this paper, an analytical approach to estimate the instantaneous frequencies of a multicomponent signal is\npresented. A non-stationary signal composed of oscillation modes or resonances is described by a multicomponent\nAM-FM model. The proposed method has two main stages. At first, the signal is decomposed into its oscillation\ncomponents. Afterwards, the instantaneous frequency of each component is estimated. The decomposition stage is\nperformed through the basis expansion exploiting orthogonal rational functions in the complex plane. Orthogonal\nrational bases are generalized to expand linear time-varying systems. To decompose the non-stationary signal, its\nequivalent time-varying system is sought. The time-varying poles of this system are required to construct appropriate\nbasis functions. An adaptive data segmentation algorithm is provided for this purpose. The effect of noise is\nscrutinized analytically and evaluated experimentally to verify the robustness of the new method. The performance of\nthis method in extraction of embedded instantaneous frequencies is asserted by simulations on both synthetic data\nand real-world audio signal
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