State space model-based harmonic decomposition of pseudo-periodic non-stationary multivariate signals

Abstract

This work is concerned with the harmonic decomposition of pseudo-periodic non-stationary multivariate signals. In this framework, a signal component corresponds to a single sinusoid with time-dependent amplitude and frequency. Thus, in the proposed harmonic decomposition, all the signal components are bound to share the same fundamental time-dependent frequency. Here, we establish a procedure to yield such decomposition by casting the multivariate signal into a block-diagonal state-space representation with multiple outputs. The harmonic components and instantaneous frequency are estimated using Kalman filtering. In addition, we provide an optimisation framework for the hyperparameters of the state space representation based on the Expectation-Maximisation algorithm. The proposed method provides an accurate, compact and physically explainable procedure for analysing pseudo-periodic non-stationary multiple-output systems, as demonstrated in the case of a simulated unbalanced rotor system and on real electrocardiographic records.