正交多小波的一种构造方法

给出一种由正交多尺度函数构造其相应正交多小波的新方法，该方法具有计算简单且不受多小波重数限制的特点，不用求解关于多元未知矩阵的非线性方程组或进行相应的多项式矩阵的因子分解。与已有的通过选取参数来确定多小波系统的方法相比，因为他由尺度序列直接确定小波序列，不必考虑改变参数时这两个序列之间相关的变化，所以更便于灵活地设计出具有各种所需特性的多小波系统。用该方法重新导出了GHM多小波。

A Method for Constructing Orthogonal Multiwavelets

A new method for constructing associated multiwavelets from multi-scaling functions is presented which is simple for computation,need not solve a set of nonlinear equations in unknown matrices or factorize correspondingly a polynomial matrix into a special form,and is not restrained by the multiplicity of multiwavelets.Unlike the methods available,it constructs two matrices from the scaling sequences,and the associated multiwavelet can be obtained by means of the two matrices.Therefore,it can be used to design multiwavelet systems with desired properties more flexibly.As an example,the authors derive the GHM multiwavelet via the new method.