Reconstruction and basis function construction of electromagnetic interference source signals based on Toeplitz‐based singular value decomposition

Abstract

In this study, the authors propose a novel method, namely Toeplitz-based singular value decomposition (or TL-SVD for short) for the reconstruction and basis function construction of electromagnetic interference (EMI) source signals. Given a specific EMI source signal, they first construct a Toeplitz type data matrix. By applying singular value decomposition (SVD) to the constructed matrix, they obtain a set of singular values, which are further divided into two parts, corresponding to the clear and noisy components of input signals, respectively. The de-noised signal can then be reconstructed by reserving relatively larger singular values and abandoning smaller ones. Finally, by utilising the compositions of certain vectors resulting from the previous SVD step, the basis function can be constructed. To evaluate the performance of the proposed method, they conduct extensive experiments on both the synthetic data and real EMI signals, by comparing with several state-of-the-art signal reconstruction methods, such as discrete wavelet transform, EEMD, sparse representation based on K-SVD and OMP. Experimental results demonstrate that the proposed method can outperform comparison approaches.