基于多分辨分析的小波紧框架构造
Wavelet Tight Frame Construction Based on Multi-Resolution Analysis
DOI: 10.12677/PM.2020.1011132, PDF,   
作者: 李 晨, 李万社：陕西师范大学，数学与信息科学学院，陕西 西安
关键词: 小波紧框架；多分辨分析；细分函数；Wavelet Tight Frame； Multi-Resolution Analysis； Refinable Function
摘要: 本文主要研究了离散序列基于多分辨分析(MRA)生成小波紧框架的构造方法。首先介绍了多分辨分析和基于多分辨分析的小波紧框架的相关知识，然后给出所定义的离散序列生成平方可积函数空间小波紧框架的充分条件，最后利用Matlab工具给出两个数值算例构造的细分函数和小波函数的函数图像。
Abstract: This paper mainly studies the construction method of tight wavelet frame generated by discrete sequences based on multi-resolution analysis (MRA). First, we introduce the related knowledge of multi-resolution analysis and wavelet tight frames based on multi-resolution analysis. And then sufficient conditions for discrete sequences are given to generate wavelet tight frame with square integrable function space. Finally, the function images of refinable function and wavelet function constructed by two numerical examples are given by Matlab.
文章引用：李晨, 李万社. 基于多分辨分析的小波紧框架构造[J]. 理论数学, 2020, 10(11): 1106-1114. https://doi.org/10.12677/PM.2020.1011132

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