| 三进制双正交对称小波的设计 |
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| 引用本文： | 王建卫,张泽银,黄达人.三进制双正交对称小波的设计[J].数学学报,2004,47(6):1089-109. |
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| 作者姓名： | 王建卫 张泽银 黄达人 |
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| 作者单位： | 1. 浙江大学数学系,杭州,310027
2. 中山大学数学系,广州,510275 |
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| 摘 要： | 本文给出了一种三进制双正交对称小波的设计方法.在给定插值紧支撑对称尺度函数的情况下,指出了如果对偶尺度函数同为紧支撑插值的,则它们同为1-型对称.并且给出了对偶尺度函数为紧支撑插值和非插值情况下的通解计算公式.还提出了频率优化方法设计对偶尺度函数和小波函数,把双正交条件归结为线性约束的二次规划问题,最后通过线性方程组来求解.对于小波函数本文也给出了一组特解公式.
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| 关 键 词： | 双正交对称小波 插值尺度函数 滤波器 |
| 文章编号： | 0583-1431(2004)06-1089-10 |
On the Construction of Triadic Symmetric Bi-Orthogonal Wavelets with Pre-Assigned Fundamental Scaling Function |
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| Jian Wei WANG Ze Yin ZHANG.On the Construction of Triadic Symmetric Bi-Orthogonal Wavelets with Pre-Assigned Fundamental Scaling Function[J].Acta Mathematica Sinica,2004,47(6):1089-109. |
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| Authors: | Jian Wei WANG Ze Yin ZHANG |
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| Institution: | Jian Wei WANG Ze Yin ZHANG (Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China) Da Ren HUANG (Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China) |
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| Abstract: | In this paper, a design method of triadic bi-orthogonal symmetric wavelets is proposed. If both dual scaling function and scaling function are compact support, symmetric and interpolatory, then they are type-1 symmetric. And the general for-mulas of compact support dual scaling functions are given. The method of frequency optimization is brought forward to design scaling function and wavelet functions. It can be formulated as linear constrained minimization problem, which can be solved through Lagrange's method of multipliers. |
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| Keywords: | Bi-orthogonal symmetric wavelets Fundamental scaling function Filter |
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