经典规范正交子波的一种简单广义化方法及其应用

从最简单的Haar尺度函数入手，提出一种简单而又快捷的方法，将每一个经典的规范正交子波基进行拓展得到一类新的规范正交子波基。新子波类中的每一个子波均继承了原始子波的许多基本性质，比如规范正交性，正则阶，时、频局域化特性等，同时也得到某些性能的改善，文中重点探讨广义Haar子波、广义Shannon子波和Meyer子波、Daubechies子波等的简单广义化；最后讨论新子波系统的一个直接应用：实（序列）信号解析子波变换的快速算法问题。

A simple method for generalizing classcal orthonormal wavelets and its applications

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.