A novel time-frequency model, analysis and parameter estimation approach: Towards multiple close and crossed chirp modes

Abstract

In this paper, a novel model for online time-frequency representation and analysis with multiple close and crossed chirp modes is proposed. It is shown that, when a signal is described by a discrete time equation, its highest time domain resolution is given by its sample interval. According to the uncertainty principle, the frequency resolution of the signal on the interval would meanwhile be nothing. However, when the amplitude and the phase of each chirp mode are taken as the state variables whose evolutions are described by a polynomial prediction model, a difference is made here. Namely, the frequency resolution can be governed by the model states and their evolutions. Based on the proposed model, it is then exemplified that an unscented Kalman filter can be used to obtain the time-frequency representation of the signal. For situations where the variance of Gaussian measurement noise is unknown or variable, a new alternative nonlinear Bayesian filtering with a simple closed form and low computational cost for doing the time-frequency analysis of the signal is presented. Simulation results verify the effectiveness of our model and analysis approach, especially in analyzing multiple close and crossed chirp modes.