Modelling of signal´s time-frequency content using warped complex-time distributions

An analytical form of the instantaneous frequency law (IFL) is very important when the physical parameters have to be evaluated from the time-frequency content of a signal. Generally, the analyzed signals are composed of several time-frequency components characterized by various nonlinear IFL. To deal with such signals, we propose a new method based on the warping operators (WO) and on the complex time distribution (CTD). Using parallel structures composed of several WO, some time-frequency components of the analyzed signal are linearized. This linearization is highlighted by using the CTD which considerably reduces the artefacts due to the complexity of the analyzed signal. This leads to an accurate estimation process, illustrated and justified by numerical and real examples.