基于Grbner基的对称正交多带多维滤波器组设计

Design symmetric orthogonal multi-band multi-dimensional filter bank using Grbner basis

通过引入计算代数中Gr bner基技术和合冲模算法,提出了一种多带多维滤波器组的多相元矩阵的对称正交化设计方法,给出了一个4带二维对称正交滤波器组的设计算例;另外,给出了由多维滤波器组构造多维小波的多维尺度方程表示形式,并将设计得到的4带二维滤波器组构造出一种4带二维小波。

This paper studied the problem of design multi-band muhi-dimensioal filter banks. Using the concept of Grobner basis and the algorithms of syzygy module in computing algebra, presented the symmetry -orthogonality approach for the polyphase matrix of multi-band multi-dimensional filter banks. Moreover, achieved the expression of multi-scale function, which was used to construct multi-wavelets by multidimensional filter banks. Constructed the 4-band two-dimensional wavelets using 4-band two-dimensional filter banks.