A simple method for generalizing classcal orthonormal wavelets and its applications
经典规范正交子波的一种简单广义化方法及其应用

A simple method which for generalizing the classical orthonormal wavelets is presented using investigation of the simplest Haar scaling function . A new kind of orthonormal wavelets is constructed from a classical orthonormal wavelets using the method proposed in this paper. These new wavelets inherit some basic properties of the corresponding classical wavelets, such as the orthonormality, the order of regularity, the time-frequency localization characteristics, and so on, meanwhile some performances of the new wavelets are improved. The generalized Haar wavelet, the generalized Shannon wavelet and the generalized Meyer wavelet, the generalized Daubechies wavelets are discussed emphatically. Finally, based on the new wavelet system, some fast algorithms for analytic wavelet transform analysis of real signals are studied.