Improved algorithm for second generation wavelet transform and its application

In order to obtain a wavelet function based on the characteristics of a set of data, an improved algorithm for the second generation wavelet transform (SGWT) is proposed by adopting the interpolating subdivision scheme and the optimum estimation theorem. For designing the predicting coefficients of SGWT, the sum of squared detail components is taken as an objective function, and the coefficients are solved by least square method with constraint of vanishing moment number for predicting. These coefficients can represent features of the given data. An optimum interpolating estimation algorithm of SGWT decomposition and reconstruction is also described. The proposed method is proved to be more effective than other wavelets for signal de-noising. It greatly improves signal noise ratio of ball bearing vibration signal in an application.