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We propose an operator-based method of adaptive signal decomposition, whereby a local narrow band signal is defined in the null space of a singular local linear operator. Based on the definition and the algorithm, we propose two types of local narrow band signals and two singular .operator estimation methods for adaptive signal decomposition. We show that our approach can solve a special case of Huang 's empirical-mode decomposition algorithm. For signals that cannot be resolved by our method or the empirical-mode decomposition algorithm, we propose a hybrid approach. Conceptually, the approach applies the empirical-mode decomposition algorithm, followed by our algorithms. Our experiments show that the proposed hybrid approach can solve a wide range of complex signals effectively.