This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes $alpha_k(t)s_k(2pi N_kphi_k(t))$ from their superposition $sum_{k=1}^K alpha_k(t)s_k(2pi N_kphi_k(t))$. First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., $alpha_k(t)$ and $N_kphi_k(t)$. 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.
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