Efficient Singular Spectrum Mode Ensemble for Extracting Wide-Band Components in Overlapping Spectral Environments

Mode decomposition methods decompose a complex signal into several principal components, which are prone to be demodulated out of non-stationary features. The efficacy of current approaches deteriorates when the components spectrally overlap, owing to their limited frequency resolution and inadequate decomposition levels. To overcome these limitations, we propose a Singular Spectrum Mode Ensemble (SME) method as an extension of the Singular Spectrum Analysis (SSA), which was traditionally considered a linear approach. The SME method employs the high-rank Hankel matrix and Singular Value Decomposition (SVD), complemented by our proposed Fast Singular Spectrum Decomposition (FSSD) and a grouping method based on Singular Value-Frequency Band correlations. Theoretical research in this paper reveals that our method achieves exceptionally high resolution in the frequency domain, facilitating the separation of the components intermixed in the spectrum. Verification experiments demonstrate our method's ability to separate non-stationary components overlapping with others in the time-frequency domain, unveiling some components in mechanical and speech signals that were previously difficult to separate and discern.