Estimation of evolutionary power spectra of univariate stochastic processes by energy-based reckoning

Abstract

In this paper a novel procedure is developed for evolutionary power spectra (EPS) estimation of univariate nonstationary stochastic processes. Specifically, the EPS is determined by estimating the statistical moments of the energy of a lightly damped linear filter excited by the nonstationary stochastic process. In this context, a smoothing procedure is incorporated by using the Savitzky-Golay (S-G) moving average filter to obtain reliable EPS based even on a limited number of available records. Further, a refinement of the approach is implemented relying on a polynomial model of temporal variation of the energy function of the filter output. Several numerical applications, involving both simulated nonstationary processes with known spectra and historical accelerograms, are used to assess the reliability and accuracy of the proposed procedure. Comparisons with the EPS estimated by a wavelets-based procedure are also provided.