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In this paper we propose a method to decompose electric power systems signals using damped sinusoids. It is inspired in the matching pursuits algorithm. The matching pursuits algorithm has the potential of decomposing a signal into coherent components. However, it is not a trivial task to obtain a decomposition which is meaningful in physical terms, as it is desirable in the case of power systems signals. We describe enhancements to the basic matching pursuits algorithm that generate decompositions in damped sinusoids with high correlation to the actual physical phenomena. We test the effectiveness of the proposed method in a signal denoising application, where the physically meaningful components are extracted from signals corrupted by noise. From the extracted components, a version of the signals almost free from noise are obtained.