Allocation of an Exponentially Modulated Harmonic from a Short Nonstationary Time Series by the SSA Method

Abstract

The method of dividing a short nonstationary time series into trend and exponentially modulated harmonic components is proposed. It is based on the SSA (Singular Spectrum Analysis) method. A feature of the method is the transformation of the original series into a new series. This is achieved by removing the trend from the original series and then double-differentiating the remainder. This procedure provides a new series of more contrasting manifestation of the harmonic component and its subsequent selection. The method is tested with polynomial trends of the second and third order. It showed high resolution, including in the presence of weak normal noise, and can be recommended for use in various physical and engineering applications for the study of harmonic processes with small coefficients of attenuation or growth.