北京航空航天大学学报 ›› 1999, Vol. 25 ›› Issue (4): 392-397.

• 论文 • 上一篇    下一篇

信号的紧小波标架表示与最佳小波基

袁运能, 毛士艺   

  1. 北京航空航天大学 电子工程系
  • 收稿日期:1998-02-01 出版日期:1999-04-30 发布日期:2010-09-28
  • 作者简介:男 36岁 博士生 100083 北京

Representation of Signal in Tight Wavelet Frame and Best Wavelet Base

Yuan Yunneng, Mao Shiyi   

  1. Beijing University of Aeronautics and Astronautics,Dept. of Electronic Engineering
  • Received:1998-02-01 Online:1999-04-30 Published:2010-09-28

摘要: 探讨了信号的小波标架表示与最佳小波基选择问题.首先对信号的小波标架表示与小波基表示的关系进行了描述,这个关系对于分析信号的小波标架表示是非常有用的;其次推导了周期小波标架的分解与重构的Mallat-塔式算法并证明了标架界为1的紧小波标架的周期化仍为标架界为1的紧小波标架;最后给出了基于小波标架算法和极小化加性代价函数的最佳小波基选择算法.

Abstract: The subject on the representation of signal in tight wavelet frame and the selection of the best wavelet base was discussed. The relation between the wavelet frame representation and the wavelet base representations, which is very useful for interpreting the wavelet frame representation, is described. then the Mallat-pyramid algorithm for periodic tight wavelet frame decomposition and reconstruction is derived and it is proven that periodic wavelet frame by periodizing the tight wavelet frame with bound 1 in is a tight wavelet frame with bound 1. Finally based on the wavelet frame algorithm and criterion of minimizing an additive cost function, the selecting best wavelet base algorithm is proposed.

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