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.
出处
《数学的实践与认识》
CSCD
北大核心
2013年第17期225-232,共8页
Mathematics in Practice and Theory
关键词
决定集
平移不变子空间
抽样定理
框架
Determining set
the shift invariant subspace
sampling theorem
frame
