Recursive Diffeomorphism-Based Regression for Shape Functions
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This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes α_k(t)s_k(2π N_kϕ_k(t)) from their superposition ∑_k=1^K α_k(t)s_k(2π N_kϕ_k(t)). First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., α_k(t) and N_kϕ_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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