Intrinsic chirp component decomposition by using Fourier Series representation

In this paper, we consider the decomposition problem for multi-component chirp signals (MCCSs). We develop a general model to characterize MCCSs, where instantaneous frequencies (IFs) and instantaneous amplitudes (IAs) of the intrinsic chirp components (ICCs) are modeled as Fourier series. The decomposition problem thus boils down to identifying the developed model. The IF estimation is addressed using the framework of the general parameterized time-frequency transform and then the signal can be easily reconstructed by solving a linear system. For the practical implementation of our method, we present a two-step algorithm, which is initiated by an iterative scheme to achieve preliminary separation of the ICCs, followed by a joint-refinement step to get high-resolution ICC reconstructions. Our method acts as a time-varying band-pass filter and can even separate ICCs that cross in the time-frequency domain. The method is applied to analyze several simulated and real signals, which indicates its usefulness in various applications.