Evaluation of the Performance of Generalized Singular Spectrum Analysis Model in Attenuation of Spectral Leakage

Singular spectrum analysis (SSA) is widely used for analyzing non-stationary signals. The SSA can be regarded as a finite impulse response (FIR) filter bank where a set of adaptive FIR filters is used to decompose the signal into several meaningful components. Some SSA components would be selected to reconstruct the signal while others would be discarded. However, the default use of a rectangular window in the conventional SSA would corrupt the frequency characteristics of the SSA components, resulting in spectral leakage. To tackle this problem, this study proposes a generalized SSA model that uses a tapered window. The window shape, determined by a non-negative real value (α), results in different levels of leakage. A positive integer parameter (p) is introduced into the SSA trajectory matrix to reduce the edge effect in the reconstructed SSA components. A two-stage grid search method is applied to find the best pair of (α,p). Experiments with synthetic signal and real electroencephalogram (EEG) signal showed that compared with the conventional SSA, the generalized SSA model with an optimal pair of (α,p) has better leakage reduction performance.