空间l^(2)(Z×Z)上正交小波基的频域特征刻画与算法  

CHARACTERIZATION AND ALGORITHMS OF ORTHONORMAL WAVELET BASES OF l^(2)(Z×Z)

作　　者：戴银云 易华[1] DAI Yin-yun;YI Hua(School of Mathematics and Physics,Jinggangshan University,Ji’an,Jiangxi 343009,China)

机构地区：[1]井冈山大学数理学院,江西吉安343009

出　　处：《井冈山大学学报（自然科学版）》2023年第4期1-6,共6页Journal of Jinggangshan University (Natural Science)

基　　金：The Scientific Research Foundation of the Education Bureau of Jiangxi Province(GJJ201009,GJJ211027);Doctoral Research Startup Project of Jinggangshan University(JZB2014);Ji'an Science and Technology Support Project(JSKJZ2014:36-13).

摘　　要：小波基的频域特征刻画有助于小波基的构造。首先给出了函数空间l^(2)(Z×Z)上正交小波基的频域特征刻画,再根据正交小波基的频域特征刻画,可以容易验证:一维空间的两个正交小波基的乘积是二维空间的正交小波基。最后还给出了完美重构条件以及快速分解重构算法。Frequency domain characterization of wavelet basis makes constructing wavelet bases painless.In this paper,such description is given for function space l^(2)(Z×Z).According to the characterization of orthogonal wavelet bases in frequency domain,it could be verified that the product of two orthogonal wavelet bases in one-dimensional space is orthogonal wavelet bases in two-dimensional space.The conditions of perfect reconstruction and the fast decomposition and reconstruction algorithm are also given.

关 键 词：正交小波基 卷积 滤波器组 完美重构 

分 类 号：O244[理学—计算数学]