A new selection method of singular values using correlation coefficients for detecting weak exponential damped sinusoidal signals under strong noise

Abstract

Weak signal detection has attracted considerable attention in a wide range of research fields, especially the weak signal detection under strong noise is an urgent problem researches are concerned with. In this paper, a new criterion to select singular values using correlation coefficient is proposed for weak exponential damped sinusoidal signal detection, which has a wide variety of signal processing applications. The innovation of our method lies in selecting K most informative singular values rather than the most energetic singular values. The proposed method measures the similarity between component signals and useful signal through autocorrelation function and correlation coefficient, which can preserve more information of the original signal and be more suitable for weak signal detection scenarios under strong noise. The numerical experiments and analysis are performed to verify the efficiency and effectiveness of our method, which indicates the proposed method is superior to the singular value selection methods based on energy or simple difference principle for correlation coefficients. Compared with stochastic resonance methods suitable for weak signal detection under strong background noise, our proposed method also has significant advantages. Thus, the proposed method is beneficial to theoretical analysis and engineering applications.