The Sliding Singular Spectrum Analysis: A Data-Driven Nonstationary Signal Decomposition Tool

Abstract

Singular spectrum analysis (SSA) is a signal decomposition technique that aims at expanding signals into interpretable and physically meaningful components (e.g., sinusoids, noise, etc.). This paper presents new theoretical and practical results about the separability of the SSA and introduces a new method called sliding SSA. First, the SSA is combined with an unsupervised classification algorithm to provide a fully automatic data-driven component extraction method for which we investigate the limitations for components separation in a theoretical study. Second, the detailed automatic SSA method is used to design an approach based on a sliding analysis window, which provides better results than the classical SSA method when analyzing nonstationary signals with a time-varying number of components. Finally, the proposed sliding SSA method is compared to the empirical mode decomposition and to the synchrosqueezed short-time Fourier transform, applied on both synthetic and real-world signals.