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Hilbert-Huang has been used as a systematic approach to analyze and characterize the temporal evolution of nonlinear, time varying process in power systems. In this paper an efficient method for analyzing the local dynamics of transient oscillations using a local empirical mode decomposition (EMD) and the Hilbert transform is presented. Two novel approaches are investigated to characterize non-stationary issues. The first technique is a local implementation of the EMD technique, through a combination of a sliding window of finite length with the sifting process by blocks. The second method is an algorithm to compute the Hilbert transform using variable window filters. Approaches to extending Hilbert-Huang analysis to analyze the local properties of non-stationary signals are explored based on finite-impulse-response (FIR) designed using Kaiser window. Through this proposed methodology is possible to make an online analysis technique for measured data using the Hilbert-Huang method. These techniques are tested on time-synchronized phasor measurements collected by PMUs. Offline technique is used in the analysis of transient phenomena emerged in power systems to compare results.