An iterative approach for decomposition of multi-component non-stationary signals based on eigenvalue decomposition of the Hankel matrix

Abstract

The decomposition of multi-component signals finds use in signal analysis. A new iterative approach to decompose a multi-component non-stationary signal into amplitude-frequency modulated (AM-FM) mono-component signals is presented in this paper. The proposed iterative approach is based on repeatedly performing eigenvalue decomposition (EVD) of the Hankel matrix, initially constructed from the samples of the multi-component signal. The components corresponding to significant eigenvalue pairs of the Hankel matrix are extracted. The process of constructing the Hankel matrix, performing EVD of the Hankel matrix and extraction of components corresponding to significant eigenvalue pairs, which we refer to as 'Iteration' is repeated till all the extracted components satisfy the defined mono-component signal criteria (MSC). The proposed decomposition approach being adaptive is suitable for analysis of non-stationary signals. The experimental results obtained by decomposing different kinds of synthetic and natural multi-component signals using the proposed iterative approach are presented and compared with the results obtained by empirical mode decomposition (EMD) and singular spectrum analysis (SSA). It is shown that unlike EMD, the ability of the proposed iterative approach to separate constituent mono-component signals is neither affected by the ratio of their mean frequencies nor by their relative amplitudes. © 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.