Cyclic Symplectic Ramanujan Component Pursuit: Algorithm and applications

Abstract

In recent years, signal decomposition method has been widely used in the engineering field to solve the problem of multimodal segmentation, such as Empirical Mode Decomposition (EMD), Ramanujan Mode Decomposition (RMD) and Adaptive Periodic Mode Decomposition (APMD) methods. Although the above methods have excellent decomposition performance, they still face many challenges for strong noise, coupled modes and other complex signals. Based on this, this paper proposes a new Cyclic Symmetric Ramanujan Component Pursuit (CSRCP) method, which can effectively decompose multi-frequency signals while protecting the integrity of the original information. First, to prevent information leakage, the circular matrix is constructed to protect the state information of the signal. Then, symplectic geometry similarity transformation is used to constrain signal decomposition, and multiple component signals with single frequency are obtained while noise reduction is performed. Finally, by constructing the Ramanujan subspace, the projection components in the Ramanujan subspace can be obtained, which enhances the extraction of periodic pulse information. The proposed method is verified by simulation and experimental signals, and the verification results show that CSRCP has superior decomposition performance.