| 引用本文： |
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丁宣浩,杨美香.两尺度矩阵与正交小波[J].广西科学,2005,12(3):172-173,176. [点击复制]
- Ding Xuanhao,Yang Meixiang.Two-Scale Matrixes and Orthogonal Wavelets[J].Guangxi Sciences,2005,12(3):172-173,176. [点击复制]
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| 摘要: |
| 设尺度函数φ(x)∈V0生成L2(R)的一个多分辨分析{Vj},W0+V0=V1,小波Ψ∈W0,两尺度关系是ϕ(x)=∑k pkϕ(2x-k),Ψ(x)=∑kqkϕ(2x-k),傅立叶变换式为ϕ(ω)=P(z)ϕ(ω/2),Ψ(ω)=Q(z)ϕ(ω/2),z=e-iω/2,两尺度矩阵为M(z)=[Q(z)P(z) Q(-z)P(-z)].{Ψ(x-k):k∈Z}为W0的标准正交基的充要条件是对几乎所有的z∈T两尺度矩阵M(z)为酉矩阵. |
| 关键词: 正交小波 两尺度矩阵 多分辨分析 构造 |
| DOI： |
| 投稿时间：2004-12-20修订日期：2005-02-17 |
| 基金项目:国家自然科学基金(10361003)资助项目。 |
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| Two-Scale Matrixes and Orthogonal Wavelets |
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Ding Xuanhao, Yang Meixiang
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| (Dept. of Comp. Sci. & Math., Guilin Inst. of Elec. Tech., Guilin, Guangxi, 541004, China) |
| Abstract: |
| Let scaling function φ(x)∈V0 yield a Multiresolution analysis {Vj} of W0+V0=V1,a small wave Ψ∈W0. The Two-scale relation is ϕ(x)=∑k pkϕ(2x-k),Ψ(x)=∑kqkϕ(2x-k), their Fourier transform is ϕ(ω)=P(z)ϕ(ω/2),Ψ(ω)=Q(z)ϕ(ω/2),z=e-iω/2,two-scale matrix is M(z)=[Q(z)P(z) Q(-z)P(-z)]. Our main result is {Ψ(x-k):k∈Z} become the standard orthogonal basis of W0 if and only if the two-scale matrix M(z) is unitary matrix for almost z∈T. |
| Key words: orthogonal wavelets two-scale matrixes multiresolution analysis structure |
