Estimation of parameters of a polynomial phase model using the warped complex time distributions

Abstract

Polynomial modelling of the phases of non-stationary signals has received recently a great deal of attention. The main future of a such model is its capability to characterize accurately a large class of time-frequency non-linearities. The estimation of the polynomial model approximating the phase of a signal is typically based on high-order ambiguity function. Since a polynomial approximation of the phase is involved, two parameters have to be previously estimated. The first one is the most appropriate order of the polynomial model. The second parameter deals with time origin within the polynomial modelling at the “optimal” order remains valid. In this paper, we propose a method to estimate these parameters which define the behaviour of polynomial order. This method is based on the joint used of warping operators and complex time argument concept.