D_4类小波的时频局部性质  

Time-Frequency Localization for D_4 Type Wavelets

作　　者：刘有明[1] 

机构地区：[1]北京工业大学应用数学系,北京100022

出　　处：《数学年刊（A辑）》2008年第1期1-14,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10671008);人才强教计划资助的项目

摘　　要：尽管小波分析已取得了许多重要成就,但主要集中在函数空间内.例如,不确定性原理的研究就是这样.然而,从应用的角度看(从图像压缩到数值计算),研究离散空间中的小波更加自然,更为重要.因此将研究离散空间l^2(Z_N)中的不确定性原理,D_4类小波以及其它一些小波的时频局部性质.Although many achievements have been made in the area of wavelet analysis, most of them focus on functional spaces. In addition, uncertainty principles always rise in those spaces. However, it is more nature and even more important to study wavelets in discrete spaces for some applications ranging from image compression to numerical analysis. This paper discusses uncertainty principles in discrete space l^2（ZN） and study timefrequency localization for D4 type wavelets and some others in the same space.

关 键 词：小波分析 不确定性原理 局部化 离散Fourier变换 

分 类 号：O174.2[理学—数学]