高阶平衡的多尺度函数和高阶Armlet的构造

The Construction of Balanced Multiscaling Function and Armlet with High Order

文章研究了多尺度函数平衡性与对应的Armlet多小波的构造,陈述了高阶平衡多尺度函数的定义与高阶Armlet多小波的定义,以及相关定理;并且证明了一个构造高阶多尺度函数的同时使得对应的多小波也是高阶Armlet的构造定理。最后,给出了一个多尺度函数是高阶平衡的同时对应多小波函数也是高阶Armlet的构造算法。

The balance of multi-scaling function and corresponding Armlet are studied in this paper. The definitions of balanced multi-scaling function with high order and Armlet multi-wavelet with high order are indicated, and some relative theorems are also stated. A constructive theorem is proved that a balanced multi-scaling function with high order can be constructed such that the corresponding multi-wavelet is Armlet with high order. Finally, an algorithm for constructing a balanced multi-scaling func-tion and corresponding Armlet with high order is given.