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

Weak signal detection has garnered considerable attention in numerous research fields, especially weak signal detection under strong noise, which is an urgent problem researches are concerned with. In this paper, a new criterion to select singular values using correlation coefficients is proposed for detecting weak exponential damped sinusoidal signals. This method has a wide variety of signal processing applications. The innovation of our method lies in selecting the most informative singular values of K rather than the most energetic singular values. The proposed method measures the similarity between component signals and useful signals via the 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. Numerical experiments and analysis are performed to verify the efficiency and effectiveness of our method, and indicate that the presented method is superior to the singular value selection methods based on energy or simple difference principle for correlation coefficients. Compared to stochastic resonance methods suitable for weak signal detection under strong background noise, our proposed method also offer significant advantages. Thus, it is beneficial for theoretical analysis and engineering applications.