Exploring the Properties of the Phase Diagram Domain for the Instantaneous Frequency Law Estimation

The characterization of non-stationary signals is usually performed using the time-frequency analysis. One fundamental feature of non-stationary signals is the Instantaneous Frequency Law. The Instantaneous Frequency Law (IFL) estimation is generally performed in time-frequency domain, by connecting the most energetic time-frequency points of the analyzed signal. With the use of the concept of phase diagram representation of a signal, which comes from the concept of nonlinear dynamic systems, our purpose is to track the Instantaneous Frequency Law of a received signal, presenting a new method for the estimation of the frequency's evolution in time. The advantage brought by this approach is the property of the phase diagram to describe the signal's phase continuity, very useful to explore for an accurate IFL tracking. In this paper, we illustrate the use of this new approach for the characterization of the digital modulations as well as in the case of overlapped signals, usual encountered in multi-path propagation channels.