In vibration measure the signal processing system of Gaussian model was abnormal for the pulse noise environment. So it was necessary to find other model and transform the traditional signal processing method. Studies showed that the Alpha stable distribution was better to describe these non-Gaussian signals. After studying the property of Alpha stable distribution and the fractional lower order statistics theory, we altered the wavelet transform. The method was that the fractional lower order statistics replaced the 2-order statistics in the traditional wavelet algorithm. Experimental vibration measure system including some sensors on the spindle or other measure points collected the vibration signals and sent to computer. The results show that the alteration wavelet transform system can effectively restrain the pulse noise and reduce the signal distortion. The new signal processing system can achieve the generalized de-noising function including re-Gaussian distribution.