Generalized Complex time-distribution using modified analytical continuation

The Generalized Complex time distributions have been recently introduced as a way for reducing the auto-terms of any bilinear time-frequency representation that appear when dealing with non-linear time-frequency structures. This concept requires the definition of signal at complex times and this abstract operation is achieved by the analytical continuation principle. In the current version, this principle is efficient only for narrow-band signals, restricting also the application of the complex time distribution to more complicate signals. The purpose of this paper is to propose a method to overcome the limitations of the analytical continuation in the case of signals with a spread time-frequency variation. This method is based on the compression of the signals spectrum to a bandwidth that ensures the efficiency of the analytical continuation technique. Then, the application of generalized complex time distribution will allow an accurate estimation of the instantaneous frequency law. The spectrum expanding will bring this estimation to the correct time-frequency location.