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Power system transients cause problems and disturbances that might be harmful to electronic equipment. However, very little has been done to systematically understand and analyze power system transients. There is also a lack of computational effective methods as transients are short and associated with a wide range of events and system conditions. This paper addresses the following issues: (1) to categorize the power system transients according to their underlying causes; (2) to propose a signal processing method, ESPRIT, for the analysis of a range of transients due to different causes. Experimental results are included to evaluate the usefulness of ESPRIT in power system transient analysis. Remaining open issues for research are also discussed.