Complex-valued differential operator-based method for multi-component signal separation

The null space pursuit (NSP) algorithm is an operator-based signal separation approach which separates a signal into a set of additive subcomponents using adaptively estimated operators and parameters. In this paper, a new operator termed complex-valued differential (CD) operator is proposed. Combining with the CD operator, this paper proposes NSP-CD algorithm to solve the CD operator-based signal separation problem. The NSP-CD algorithm can separate the multi-component signal into sum of amplitude-modulated and frequency-modulated (AM-FM) signals in the form of A(t)exp(j)(ϕ(t)). The proposed NSP-CD algorithm has many advantages. Firstly, the proposed CD operator can ensure that the AM-FM signal totally lies in the null space of the operator rather than close to the null space that the original used operator may reach. Secondly, compared with the original NSP algorithm, our algorithm provides a more reasonable strategy to update the regularization parameter λ and the leakage factor γ. Finally, we have proved that the proposed algorithm has quadric convergence theoretically. Experiments on both synthetic and real-life signals demonstrate that the NSP-CD algorithm is more robust and effective than other state-of-the-art methods.