Diagonal time dependent state space models for modal decomposition of non-stationary signals

Abstract

This work is devoted to the problem of the decomposition of a non-stationary signal into modal components, for which a methodological approach based on diagonal time-dependent state space models is postulated. In particular, on this paper is shown that the response of a diagonal time-dependent state space models can be cast into a modal form characterized by time-dependent amplitudes and frequencies. Later, a Kalman filter based framework for non-stationary modal decomposition is built on the previously discussed diagonal state space representations. The enhanced performance of the proposed methods is demonstrated on a benchmark test consisting of three non-stationary modal components, and on the modal decomposition and denoising of a ElectroCardio Graphic signals from the QT database. The proposed methods constitute a reliable tool for on-line modal decomposition of multi-component non-stationary signals, with results comparable and even better than other state-of-the-art methods.