Varying Wave-Shape Component Decomposition: Algorithm and Applications

The decomposition problem for multiple sinusoidal component signals has been developed in the past decades. However, many complex time series are made up of wave-shape components, which invalidates signal decomposition methods based on sinusoidal components. Since wave-shape components are time-varying from one cycle to the other and often contaminated by strong noise, robustly decomposing a signal into wave-shape components is still a challenging task. In this article, a varying wave-shape component decomposition (VWCD) method is proposed to extract time-varying and weak characteristics of wave-shape components from a multicomponent signal. Specifically, instantaneous frequencies (IFs) of varying wave-shape components are no longer inter multiples of a fundamental IF allowing the VWCD method more flexible in practical applications. We propose an instantaneous amplitudes and fundamental component phases estimation method based on an intrinsic chirp signal model and a regression coefficients initialization method by a fixed wave-shape signal model. The potential and effectiveness of the proposed VWCD method are verified by some simulated signals with different signal-to-noise ratios, a real-world electroencephalography seizure signal, and an experimental chest wall vibration signal from a microwave vital sign monitoring system.