On the use of Singular Spectrum Analysis

Abstract

Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix estimated after embedding the signal into its delayed coordi- nates. In this work we show that the eigenvectors can be used to calculate the coefficients of a set of filters which form a filter bank. The properties of these filters are derived. In particular we show that their outputs can be grouped according to their frequency response. Furthermore, the fre- quency at the maximum of each frequency response and the corresponding eigenvalue can provide a power spectrum estimation of the time series. Two different applications illustrate how both characteristics can be applied to analyze wideband signals in order to achieve narrow-band signals or to infer their frequency occupation.