The characteristics of singular values of alternating current, direct current and noise components when Hankel matrix is used in singular value decomposition (SVD) are studied respectively. It’s pointed out that if the order of matrix is big enough, the singular values representing these three components will be isolated as independent coordinates in the total singular value vector, and there are sudden changes in the joints of these coordinates. It’s proposed that this total singular value vector be processed by quadratic spline wavelet transform, and then the effective singular values can be determined by the peak position of wavelet detail signal. The studying results show that if the maximum peak happened in the second coordinates, then it means that a major direct current component is existed in the original signal and under this circumstance the number of effective singular values will be determined by the second maximum peak position, otherwise the number of effective singular values is determined by the maximum peak position. Signal processing examples demonstrate the effectiveness of this method, and the processing result for the vibration signal of bearing shows that a modulated signal is isolated successfully from the strong background noise and the injuring state of roll track of this bearing is diagnosed reliably according to this modulated signal.