  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.
