Basis approach to estimate the instantaneous frequencies in multicomponent AM-FM signals

Abstract

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