正交复滤波器与小波的数值构造

Numerical method for constructing orthogonal complex filter banks and wavelets

研究了参数化正交复滤波器与小波的数值构造方法.在以往研究成果的基础上,建立了构造正交复滤波器的蝶形算法,该算法便于计算任意长度紧支集复滤波器,便于优化参数设计所需的滤波器与小波.并且研究了参数变化与复滤波器性质的关系,给出相关定理并加以证明.最后给出不同参数下复滤波器、复尺度函数和复小波的计算实例,通过参数优化得到具有对称性和近似线性幅频特性的复小波函数.

The numerical methods for constructing the parameterized orthogonal complex filter banks and wavelets were investigated in this paper. Based on the Ref , a so-called papilionaceous algorithm for constructing the orthogonat complex filter banks is presented, which was used to easily design orthogonal complex filter banks and wavelets on arbitrary length compactly supported sets by the optimizations of the parameters. The relationships between the properties of complex filter banks and the parameters were discussed and the theorems about them were proved. The complex filter banks, scale functions and wavelets with various parameters are calculated in the example. The orthogonal complex wavelets with the symmetric property and approximately linear phase are obtained by the parameter optimizations.