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采样定理在数字信号通讯中发挥了十分重要的作用,因为信号通常由它的离散采样数据来恢复.Han Bin等人在[J.Comput.Appl.Math.,2009,227:254-270]中构造了广义插值加细函数向量.本文研究与广义插值加细函数向量有关的采样定理的拓展问题.具体而言,对于已知的广义插值d-加细函数向量φ=(φ_1,…,φ_r)~T,即φe(m/r+k)=δ_kδ_(e-1-m),k∈Z,m=0,1,…,r-1,e=1,…,r我们将构造一组函数{φ_(r+1),…,φ_(dr)},使得φ~ロ=(φ~T,φ_(r+1),…,φ_(dr))~T也是d-加细的,而且满足φ_e(m/(dr)+k)=δ_kδ_(θ_(d,r(e)-m))k∈Z,m=0,1,…,dr-1,e=r+1,…,dr,其中θ_(d,r(e))=e-r+R_(e-1-r,d-1),R_(e-1-r,d-1)=「(e-1-r)/(d-1)」.我们建立与φ~■有关的采样定理.显然,φ的多小波子空间采样定理的适用范围得到了拓展.给出φ~■的多小波子空间采样级数的截断误差估计.
The sampling theorem plays a very important role in digital signal communication because the signal is usually recovered from its discrete sample data. Han Bin et al. [J. Comput. Appl. Math., 2009, 227: 254-270] The generalized interpolation and fine function vectors are constructed. In this paper, the expansion of the sampling theorem related to the generalized interpolation and fine function vectors is studied. Specifically, for the known generalized interpolated d-summing function vectors φ = (φ_1, ..., φ_r ) ~ T, ie φe (m / r + k) = δ_kδ_ (e-1-m), k∈Z, m = 0,1, ..., r-1, e = 1, ..., r We will construct A set of functions {φ_ (r + 1), ..., φ_ (dr)} such that φ_ro = (φ ~ T, φ_ (r + 1), ..., φ_ (dr)) ~ T are also d- , And satisfies φ_e (m / (dr) + k) = δ_kδ_ (θ_ (d, r (e) -m)) k∈Z, m = 0,1, ..., dr- 1, ..., dr, where θ_ (d, r (e)) = e-r + R_ (e- 1 -r, d- 1), R_ (e- 1 -r, d- 1) = “ -1-r) / (d-1). ”We establish a sampling theorem related to φ ~ ■ Obviously, the scope of the multi-wavelet subspace sampling theorem for φ has been extended. Truncation Error Estimation of Spatial Sampling Series.