有决定集和平移不变子空间中抽样定理

Determining Set and Sampling Theorem in the Shift Invariant Subspace

研究了抽样间隔为a(0≤a<1)的平移不变子空间中的抽样定理.首先,给出了平移不变子空间的决定集的一个刻画,然后,通过平移不变子空间的决定集,给出了函数属于一个抽样空间的充要条件.

In this paper we study sampling theorem in the shift invariant subspace. Firstly, Determining set in the shift invariant subspace are classified; Then, by determining set in the shift invariant subspace, a sufficient and necessary condition that a function helongs to a sampling space is given.