小波基和它对一维信号的直接分解(Ⅱ)  

Wavelet Bases and Direct Wavelet Decomposition of One Dimensional Signals(Ⅱ)

作　　者：陈志奎[1] 徐铭陶[1] 秦树人[1] 汤宝平[1] 

机构地区：[1]重庆大学测试中心

出　　处：《重庆大学学报（自然科学版）》1998年第4期65-72,共8页Journal of Chongqing University

基　　金：国家自然科学基金

摘　　要：研究了两类Ｉ．Ｄａｕｂｅｃｈｉｅｓ规范正交小波，一类Ｒ．Ｃｏｉｆｍａｎ小波和Ｙ．Ｍｅｙｅｒ及三种具有解析表达式的小波（ＭｅｘｉｃａｎＨａｔ小波、Ｈａａｒ小波和ＬｉｔｌｅｗｏｏｄＰａｌｅｙ小波）和它们生成的小波基的几种重要的特征（小波矩、消失矩、局部化特性、线性相位等）参数；针对一维信号的小波变换，对各种小波进行了评估，推荐出针对满足不同要求的较佳的小波；并对信号的小波分解分量及其Ｆｏｕｒｉｅｒ变换作了比较。Several important characteristics (wavelet moment, vanishing moment, localization property,linear phases, etc.)of two class I.Daubechies orthonormal wavelets,one class Coifman wavelets , Y.Meyer wavelet and three analytical wavelets (Haar wavelet、Littlewood-Paley wavelet and Mexican hat wavelet) and their created wavelet bases are researched in details.For wavelet transform of one dimensional signals,each basis is appraised via comparison and the best wavelet basis is recommended.Decomposition components and their Fourier transforms of one dimensional signals wavelet transforms are compared in different frequency ranges.

关 键 词：小波基 局部化特性 直接小波分解 信号 

分 类 号：O174.2[理学—数学] TN911.1[理学—基础数学]