Weak Signal Extraction in Noise Using Variable-Step Gaussian-Sinusiodal Filter

When analyzing vibration or acoustic signals in machinery, noise interference within the characteristic signals can significantly distort the results. This issue is particularly pronounced in complex environments, where mechanical signals are often overwhelmed by noise, making it extremely difficult or even impossible to determine the operational status of mechanical equipment by the analysis of characteristic signals. Existing methods for analyzing weak signals in the presence of strong Gaussian noise have limitations in their effectiveness. This paper proposes an innovative approach that utilizes a Variable-Step Gaussian-Sinusoidal Filter (VSGF) combined with rotational coordinate transformation to extract weak signals from strong noise backgrounds. The proposed method improves noise reduction capabilities and frequency selectivity, showing significant improvements over traditional Gaussian filters. Experimental validation demonstrates that the signal detection accuracy of the proposed method is 10-15% higher than that of conventional Gaussian filters. This paper presents a detailed mathematical analysis, experimental validation, and comparisons with other methods to demonstrate the effectiveness of the proposed approach.