Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions
Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions
LI Hu-an1, FANG Gen-sun2
1.College of Sciences, North China University of Technology, Beijing 100041, China; 2.School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
Abstract：Denote by B2σ,p(1 < p < " ) the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [-?, ?]. It is shown that a function in B2σ,pcan be reconstructed in Lp(R) by its sampling sequences {f(k?/?)}k∈Z and{f 2(k?/?)}k∈Z using the Hermite cardinal interpolation. Moreover, it will be shown that if f belongs to Lpr(R), 1 < p < ∞, then the exact order of its aliasing error can be determined.
出版日期: 2006-06-05
引用本文:
. Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions[J]. Frontiers of Mathematics in china, 2006, 1(2): 252-271.
LI Hu-an, FANG Gen-sun. Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions. Front. Math. China, 2006, 1(2): 252-271.
