中文摘要：

将2尺度正交多小波有m逼近阶的定义推广到尺度因子为a（a≥2）的情形,给出了a尺度正交多小波具有m阶逼近阶的充分必要条件,研究了a尺度矩阵符号的分解;在此基础上根据a尺度正交多尺度函数的m阶平衡性的定义,给出了三个a尺度正交多小波具有m阶平衡阶的充分必要条件;然后,对理论结果通过例子进行了验证.

英文摘要：

Generalizing the definition of m-order approximation of two-scale orthonormal multiwavelets to the case that the scale factor is equals to a（a≥2）,a sufficient and necessary condition is proposed for orthonormal multiwavelets with scale a to have m-order approximation, by studying the factorization of a-scale matrix symbol;Based on the m-balanced definition of orthonormal multiscaling functions with scale a,three sufficient and necessary conditions are investigated for such orthonormal multiwavelets to have m-order balance;Then,verify the theory by means of an example.