二进小波变换的卷积定理(英文)  

The Convolution Theorem for Dyadic Wavelet Transform

作　　者：石智[1] 魏恒东[1] 郑建国[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《应用数学》2006年第3期569-574,共6页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (10071068)

摘　　要：本文研究二进小波变换在信号处理中的应用.首先证明了两个满足容许性条件和规范性条件的二进小波的卷积和相关仍满足容许性和规范性条件,然后证明了二进小波变换的卷积定理和相关性定理,最后给出数值例子说明二进小波变换的卷积定理在加噪信号重构中的优越性.Applications of dyadic wavelet transform to signal processes is studied. We first show that the convolution and correlation of two dyadic wavelets who satisfy admissibility and regularity condition satisfy the admissibility and regularity condition, and then we derive the convolution and correlation theorem for the dyadic wavelet transform. Finally, we present numerical example showing the usefulness of applying the convolution theorem for the dyadic wavelet transform to perform signal restoration in the presence of additive noise.

关 键 词：傅立叶变换 二进小波 卷积 相关 

分 类 号：O241.5[理学—计算数学]