Decomposing non-stationary signals with time-varying wave-shape functions

Abstract

Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude. The signal processing mission is further challenged if each component has oscillatory pattern far from a sinusoidal function. In biomedical field, the oscillatory pattern is even changing from time to time and contaminated by noise. In practice, if multiple components exist, it is desirable to robustly decompose the signal into each component for various purposes, and extract desired information. Such challenge have raised a significant amount of interest in the past decade, but a satisfactory solution is still lacking. We propose a novel nonlinear regression scheme to handle such challenge. In addition to simulated signals, we show its applicability to two physiological signals, impedance pneumography and photoplethysmogram, and examine how acutely the proposed decomposition scheme help extract physiological information. Comparisons with existing solutions, including linear regression, recursive diffeomorphism-based regression and multiresolution mode decomposition, supports the advantages for our proposal.