Study on Interpolating Condition and Balance of Multiwavelet

程蓉; 赵宇; 李万社

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Study on Interpolating Condition and Balance of Multiwavelet

更新时间：2026-09-14

- Study on Interpolating Condition and Balance of Multiwavelet
- 多小波的插值条件与平衡性研究
- Vol. 30, Issue 2, Pages: 110-114(2009)
- 作者机构：
  
  1. 中北大学理学院
  2. 中北大学信息与通信工程学院
  3. 陕西师范大学数学与信息科学学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2009
- 稿件说明：
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程蓉, 赵宇, 李万社. Study on Interpolating Condition and Balance of Multiwavelet[J]. 2009, 30(2): 110-114.
DOI：

程蓉, 赵宇, 李万社. Study on Interpolating Condition and Balance of Multiwavelet[J]. 2009, 30(2): 110-114. DOI：

摘要

在简要分析多小波的逼近性与平衡性的基础上

通过简短的证明得出了具有一定平衡阶的多小波系统

其相应的多尺度函数必具有相同阶逼近的结论.在引入了多小波不同于单小波的插值条件后

得到具有一定逼近阶的多尺度函数

如果同时满足插值条件

则相应系统必然具有相同的平衡阶的结论.

Abstract

On the basis of a simple analysis of approximation and balance of multiwavelet

a simple proof is given to deduce that a multiwavelet system with given balancing order must have a multiscaling function with the same approximation order.After introducing the special interpolating condition of multiwavelet

the conclusion is that if a multiscaling function has a given approximation order and satisfies the interpolating condition simultaneously

the corresponding system consequentially has the same balancing order.

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references

Goodman T N T,Lee S L.Wavelets of multiplicity r[J].Transactions of the American Mathematical Society,1994,342(1):307-324.

Strela V.Multiwavelets:Theory and applications[D].Department of Mathematics,Massachusetts Institute ofTechnology,Cambridge,MA,1996.

Jé^rome Lebrun,Martin Vetterli.Balanced multiwavelets theory and design[J].IEEE Transactions on SignalProcessing,1998,46(4):1119-1125.

Jé^rome Lebrun,Martin Vetterli.High-order balanced multiwavelets:theory,factorization,and design[J].IEEETransactions on Signal Processing,2001,49(9):1918-1929.

Geronimo J S,Hardin D P,Massopust P R.Fractal functions and wavelet expansions based on several scalingfunctions[J].Journal of Approximation Theory,1994,78(3):373-401.

Stéphane Mallat.信号处理的小波导引[M].第2版.杨力华译.北京:机械工业出版社,2002.

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