二维平移不变子空间中的广义抽样定理  

General Sampling Theorem in the Shift Invariant Subspace in Two Dimensions

作　　者：郝祥晖[1] 李坤花[1,2] 

机构地区：[1]济源职业技术学院基础部,河南济源454650 [2]郑州大学数学系,河南郑州450001

出　　处：《数学的实践与认识》2013年第17期225-232,共8页Mathematics in Practice and Theory

摘　　要：抽样定理在数字信号处理和图像处理中具有重要的作用,古典Shannon抽样定理因其局限性而限制了它的应用.本文研究了二维平移不变子空间中以任意点作为抽样点的规则抽样定理.首先,抽样空间的一些特征被给出;接着,平移不变子空间的决定集的一个刻画被得到.然后,通过平移不变子空间的决定集,函数属于一个抽样空间的充要条件被证明.Sampling theorem plays an important role in digital signal processing and image processing, but classical Shannon sampling theorem has its disadvantage in application. In this paper, sampling theorem in the shift invariant subspace in two dimension is studied. Firstly, some characterizations of sampling space are given. Then, determining set in the shift invariant subspace is classified. At last, by determining set in the shift invariant subspace, a sufficient and necessary condition that a function belongs to a sampling space is obtained.

关 键 词：决定集 平移不变子空间 抽样定理 框架 

分 类 号：TN911.7[电子电信—通信与信息系统] O212.2[电子电信—信息与通信工程]