  The adaptive non-harmonic (ANH) model is a powerful tool to compactly
represent oscillating signals with time-varying amplitude and phase, and
non-sinusoidal oscillating morphology. Given good estimators of instantaneous
amplitude and phase we can construct an adaptive model, where the morphology of
the oscillation is described by the wave-shape function (WSF), a
2{\pi}-periodic more general periodic function. In this paper, we address the
problem of estimating the number of harmonic components of the WSF, a problem
that remains underresearched, by adapting trigonometric regression model
selection criteria into this context. We study the application of these
criteria, originally developed in the context of stationary signals, to the
case of signals with time-varying amplitudes and phases. We then incorporate
the order estimation to the ANH model reconstruction procedure and analyze its
performance for noisy AM-FM signals. Experimental results on synthethic signals
indicate that these criteria enable the adaptive estimation of the waveform of
non-stationary signals with non-sinusoidal oscillatory patterns, even in the
presence of considerable amount of noise. We also apply our reconstruction
procedure to the task of denoising simulated pulse wave signals and determine
that the proposed technique performs competitively to other denoising schemes.
We conclude this work by showing that our adaptive order estimation algorithm
takes into account the interpatient waveform variability of the
electrocardiogram (ECG) and respiratory signals by analyzing recordings from
the Fantasia Database.
