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An important feature of an oscillation is the damping characterization. For a system, the damping characteristic of the oscillation that occurs on its states or outputs gives the information of the stability of the system. There are various techniques to compute the damping ratio of a linear model of a system, but the tools that apply to nonlinear systems are scarce. In this paper, we utilize the Hilbert transform of nonlinear and nonstationary oscillatory signals to compute the instantaneous damping of the signals. The technique is applied to the computation of the damping ratio of power systems signals that contain inter area oscillations. This damping computation is important for power system monitoring.