一类紧支撑正交多小波的显式构造

Explicit Construction of First Class Compact Supported Orthogonal Multi Wavelets

以所构造的正定矩阵为基础,给出了2尺度紧支撑正交多小波的构造方法,证明了当2尺度r重紧支撑正交多尺度函数的系数矩阵Pi是r×r阶可逆矩阵,存在正交矩阵A,使PiPTi与diag(λi,1,λi,2,…,λi,r)合同。算例的结果说明,当AT(2I-PiPTi)-1 PiPiTA是对角的正定矩阵时,可构造出2重紧支撑正交多小波函数。

Based on the constructed positive definite matrix,construction method of compact supported orthogonal multi wavelets with dilation factor 3are presented to prove that coefficient matrix of compact supported orthogonal multi-scaling functions with dilation factor 2is an invertible matrix with order,and orthogonal matrix exists in making same with.The result of example indicates that 2compact supported orthogonal multi-wavelet function can be constructed when is diagonal positive definite matrix.