Recursive Diffeomorphism-Based Regression for Shape Functions

Abstract

This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes ${\alpha }_k(t)s_k(2\pi N_k{\varphi }_k(t))$ from their superposition ${\sum }_{k=1}^K{\alpha }_k(t)s_k(2\pi N_k{\varphi }_k(t))$. First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., ${\alpha }_k(t)$ and $N_k{\varphi }_k(t)$. Second, a novel approach based on diffeomorphisms and nonparametric regression is proposed to estimate wave shape functions $s_k(t)$. These two methods lead to a framework for the generalized mode decomposition problem under a weak well-separation condition. Numerical examples of synthetic and real data are provided to demonstrate the fruitful applications of these methods.

References in corpus (4)

• Empirical wavelet transform
• ConceFT: Concentration of Frequency and Time via a multitapered synchrosqueezed transform
• Extracting a shape function for a signal with intra-wave frequency modulation
• Wave-shape function analysis -- when cepstrum meets time-frequency analysis

Cited by in corpus (1)

• Multiresolution Mode Decomposition for Adaptive Time Series Analysis