基于Grobner基与合冲模方法的M-带对称正交小波设计

M-band Symmetric Orthogonal Wavelets Design via Grobner Basis and Syzygy Module

通过引入计算代数中Grobner基以及合冲模的相关算法,提出对多相位矩阵进行正交化,从而得到了同时具有对称性和任意正则阶的M-带正交小波的高效设计方法。与现有方法相比,克服了构造过程复杂以及不能保持线性相位的缺陷。

We present a method to design symmetric orthogonal M-band wavelets with arbitrary regularity by using Grobner basis and Syzygy module algorithm in computing algebra to orthogonalize the polyphase matrix. By using the existing methods, the computational process is complicated and the linear-phase cannot be achieved. These drawbacks can be overcome by using the new one.