Evolutionary Spectra Estimation of a Nonstationary Process Based on a Single Sample

Abstract

This paper proposes a novel method for estimating the evolutionary power spectral density (EPSD) of a nonstationary process based on a single sample. In the proposed method, a sample of a nonstationary process is decomposed into several components with a new binomial fitting decomposition (BFD). The EPSD of each component can be estimated using a newly proposed time-varying standard deviation estimation method and short-time Thomson multiple-window spectrum estimation method. The EPSD of the analyzed nonstationary sample is obtained by combining the EPSDs of all components. Via a comprehensive numerical study, the applicability of the proposed EPSD estimation method (for estimating the EPSD of a nonstationary process) is analyzed and compared with those by the Priestley method and wavelet-based method. The numerical results indicate that the estimated EPSD by the proposed method is more consistent with the corresponding theoretical one than those by the other two methods. Finally, the EPSDs of Storm Ampil, measured atop the Shanghai World Financial Center, are analyzed by the proposed method.