Abstract: The symmetric biorthogonal low-pass filters of 4-band and the corresponding scaling functions are constructed by using the sum rules. Also, the symmetric or anti-symmetric biorthogonal wavelet filters of 4-band with high order vanishing moment and short support are obtained. Especially, the coefficients of filter constructed are all rational numbers and their denominators are all binary. Therefore, it is very convenient for these filters to be applied. At last, the smoothness index of the scaling functions constructed can be estimated by the method of Hanbin.

Key words: biorthogonal wavelets, filters, sum rules

摘要： 利用求和法则设计了四带对称的双正交低通滤波器及其对应的尺度函数,并得到了满足对称性或反对称性、具有较高阶消失矩和较短支集的四带双正交小波滤波器；特别指出的是所构造的滤波器系数为有理数,而且分母是二进数,给应用带来很多方便。另外还利用Hanbin的方法估算出了所构造的尺度函数的光滑指标。

关键词: 双正交小波, 滤波器, 求和法则