The state models of the SKF6205-2RS deep groove ball bearing are set to predict the location and degree of its damage based on the Hertzian contact deformation theory, elastic theory and the geometry of the rolling bearing. Next, the system response is obtained using the Runge-Kutta numerical method. The calculation results prove that the frequency and harmonic components of the local damages of the inner ring, outer ring and ball under radial loads are well predicted. Moreover, the bearing vibration laws under different conditions are introduced to prove the periodicity of the continuous Haar wavelet transform. Finally, an autocorrelation continuous Haar wavelet method is proposed for early damage signals exacting of rolling bearings. The proposed approach is successfully applied to noise reduction and weak impulse feature extraction of bearing signals.