紧支正交小波的参量化法和波数字滤波器

The Parametrization of Orthonormal Compactly Supported Wavelets and Wave Digital Filter

本文详细分析了小波变换，镜像滤波器（ｑｕａｄｒａｔｕｒｅｍｉｒｏｒｆｉｌｔｅｒ－ＱＭＦ）组和波数字滤波器散射矩阵之间的关系，提出了由散射矩阵的基本因子来构造镜像滤波器对，从而得出了具有任意消失矩的紧支正交小波的参量化法。并给出了基于正则性约束的参量优化和一个有效的实现小波变换的格型结构。

In this paper,the close relationship among wavelet transform,quadrature mirror filter(QMF)banks and the scattering matrix of wave digital filter(WDF) is analyzed in detail.The parametrization of orthonormal compactly supported wavelet bases that have an arbitrary number of vanishinw moment is obtained by building any QMF pair out of elementary factors of the scattering matrix.In addition,the optimization of parameter and the efficient lattice structure to implement the transform are also presented.