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

Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern, or the wave-shape function, far from a sinusoidal function, and the oscillatory pattern is even changing from time to time. In practice, if multiple components exist, it is desirable to robustly decompose the signal into each component for various purposes, and extract desired dynamics information. Such challenges have raised a significant amount of interest in the past decade, but a satisfactory solution is still lacking. We propose a novel {\em nonlinear regression scheme} to robustly decompose a signal into its constituting multiple oscillatory components with time-varying frequency, amplitude and wave-shape function. We coined the algorithm {\em shape-adaptive mode decomposition (SAMD)}. In addition to simulated signals, we apply SAMD to two physiological signals, impedance pneumography and electroencephalography. Comparison with existing solutions, including linear regression, recursive diffeomorphism-based regression and multiresolution mode decomposition, shows that our proposal can provide an accurate and meaningful decomposition with computational efficiency.