最小能量多重仿射紧框架的特征  

Characterization of Mminimum-Energy Multiwavelet Tight Frames

作　　者：王慧 张松俊 程正兴[2] WANG Hui;ZHANG Song-jun;CHENG Zheng-xing(Normal School, Nanyang Institute of Technology, Nanyang 473000, China;School of Math. and Statistics, Xi＇an Jiaotong University, Xi＇an 710049, China)

机构地区：[1]南阳理工学院师范学院,河南南阳473000 [2]西安交通大学数学与统计学院,陕西西安710049

出　　处：《数学的实践与认识》2017年第21期245-253,共9页Mathematics in Practice and Theory

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

摘　　要：引入多个加细函数生成的最小能量多重仿射框架的概念.运用矩阵理论和时频分析方法,给出对应于最小能量多重仿射框架的多重加细函数所满足的条件.得到最小能量多重仿射紧框架的特征与构造方法.对原多重加细函数和最小能量多小波仿射框架做正交变换,得到新的多重加细函数和对应的最小能量多重仿射框架.The concept of minimum-energy multiple affine frames which are generated from multiple refinable functions is introduced. The conditions which are satisfied by multiple refinable functionsassociated with minimum-energy multiple affine frames are provided with the help of matrix theory and time-frequency analysis. Characterizations and constructive methods for minimum-energy multiple tight affine frames axe derived. A new multiple re- finable functions and corresponding minimum-energy multiple tight affine frames axe ob- tainedthrough implementing orthogonal transform on the given multiple refinable functions and the minimum-energy multiple tight affine frames.

关 键 词：多重仿射框架 多重加细函数 正交变换 傅立叶变换 矩阵面具 滤波器 

分 类 号：O174.2[理学—数学]