广义加细函数与广义小波函数的分解与重构算法  

Decomposition and reconstruction algorithms of generalized refinement functions and generalized wavelet functions

作　　者：于育民 段志霞[2] 程正兴[3] YU Yu-min;DUAN Zhi-xia;CHENG Zheng-xing(School of Math. and Statistics,Nanyang Institute of Technology,Nanyang 473004,China;Dept. of Fundamentals,Jiyuan Vocational and technical College,Jiyuan 464650,China;School of Math. and Statistics,Xi'an Jiaotong University,Xi'an 710049,China)

机构地区：[1]南阳理工学院数学与统计学院,河南南阳473004 [2]济源职业技术学院基础部,河南济源464650 [3]西安交通大学数学与统计学院,陕西西安710049

出　　处：《兰州理工大学学报》2018年第6期151-157,共7页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(61403298);河南省自然科学基金(102300410022)

摘　　要：引入广义加细函数与广义小波函数的概念.运用时频分析方法与分数阶小波变换,研究分数阶多进制正交小波的存在性与构造方法,得到广义多进制正交小波存在的一个充要条件.提出广义加细函数与广义小波函数的分解与重构算法.The concept of generalized refinement function and wavelet function is introduced into this article.Existence and constructive methods for fractional multi-scale orthogonal wavelets are investigated by means of time-frequency analysis method and fractional wavelet transform and a sufficient and necessary condition for its existence is obtained.The decomposition and reconstruction algorithms of the generalized refinement function and wavelet function are proposed.

关 键 词：分数阶傅立叶变换 广义小波函数 广义加细函数 分数阶小波变换 时频分析 

分 类 号：O174.2[理学—数学]