Frequency and amplitude tracking for short nonstationary and nonlinear signals

Whatever the application domains, when dealing with strongly nonstationary and nonlinear signals, Fourier-based methods and even classical time-frequency methods are no longer able to estimate and track the instantaneous amplitudes and frequencies of each signal component. One possibility to get away from the Heisenberg incertitude constraint is to set a model, which has to be as general as possible in order to be valid in many domains. In that context, we have proposed and studied a new model, which writes as a time-varying polynomial-amplitude and polynomial-phase signal. Parameter estimation is casting as the maximisation of the likelihood function, which is overcome by meta-heuristic approaches, such as simulating annealing. In that paper, based on simulations, we detail the performance of the Short Local Polynomial model-based method (Short-LP) we proposed for a number of particular cases when analysing one or two components on very short-time duration. We first assess the frequency resolution limit when analysing close frequency-modulated components. The performance is explained according to classical Fourier limits and more particularly the dynamic signal bandwidth, the signal being nonstationary. The analysis of amplitude-modulated components is then discussed according to the presence or not of the carrier frequency. Finally, we stress upon the performance of the amplitude estimation in the particular case where the instantaneous frequencies are known a priori.