Abstract: A new method for extracting fault features of rolling bearings is proposed, which combines covariance matrix, singular value difference spectrum, and singular value median decomposition, to address the difficulty of extracting weak fault feature information from rolling bearings due to noise interference. Firstly, considering the fault characteristics of rotating machinery, a 1-step method is used to construct a Hankel matrix for bearing fault signals. Secondly, considering the advantage of the signal covariance matrix for signal autocorrelation denoising, the Hankel covariance matrix is calculated and phase space reconstruction is performed. Thirdly, the singular value difference spectrum method is used to decompose and process the reconstructed covariance matrix signal to achieve preliminary noise reduction. The singular value median decomposition method is used to decompose and filter it to complete secondary noise reduction. Based on the spectral envelope of the processed signal, bearing fault feature information is extracted. Finally, through the analysis of experimental data on rolling bearings, the results show that the proposed method can effectively extract the fault characteristics and harmonics of noise signals, achieve effective extraction of different types of bearing fault characteristics, and provide a new method and approach for complex signal processing and diagnosis of rolling bearing faults.