In this paper a novel approach is developed for the determination of evolutionary power spectra (EPS) of non-stationary random processes that can be used as models of earthquake accelerograms. Specifically, the spectra are estimated by considering the statistical moments of the energy of lightly damped linear systems (filters) excited by the stochastic seismic process. In this manner, an estimate of the EPS of the seismic input is derived by varying the frequency of the linear system. For this purpose, an appropriate smoothing procedure is also incorporated, relying on the use of the so-called Savitzky-Golay moving average filter. This is done for obtaining reliable spectra based on a relatively small number of available records. Further, a possible refinement of the approach is investigated introducing a polynomial representation for the mean energy of the filter output. Finally, several examples involving both simulated data with known target spectrum, and measured data are used to show the usefulness and reliability of the proposed approach.