Complex-analytic approach to the sinc-Gauss sampling formula

被引：18

作者：

Tanaka, Ken'ichiro ^{[1
]}

Sugihara, Masaaki ^{[1
]}

Murota, Kazuo ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Dept Math Informat, Tokyo 1138656, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2008年 / 25卷 / 02期

关键词：

sampling formula; sinc-Gaussian kernel; sinc numerical methods;

D O I：

10.1007/BF03167520

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with theoretical error estimates for a sampling formula with the sinc-Gaussian kernel. Qian et al. have recently given an error estimate for the class of band-limited functions by Fourier-analytic approach. In contrast, we adopt in this paper a complex-analytic approach to derive an error estimate for a wider class of functions including unbounded functions on R. Part of the result of Qian et al. can be derived from ours as an immediate corollary. Computational results show a fairly good agreement with our theoretical analysis.

引用

页码：209 / 231

页数：23

共 15 条

[1]

[Anonymous], SAMPL THEORY SIGNAL

[2]

HIGGINS JR, 1996, SAMPLING THEORY FOUR

[3]

Qian Liwen, 2006, Sampling Theory in Signal and Image Processing, V5, P1

[4] Localization of the generalized sampling series and its numerical application [J].

Qian, LW ;

Creamer, DB .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 43 (06) :2500-2516

[5] On the regularized Whittaker-Kotel'nikov-Shannon sampling formula [J].

Qian, LW .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (04) :1169-1176

[6] Summary of Sinc numerical methods [J].

Stenger, F .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 121 (1-2) :379-420

[7]

Stenger F., 1993, NUMERICAL METHODS BA

[8] Recent developments of the Sinc numerical methods [J].

Sugihara, M ;

Matsuo, T .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 164 :673-689

[9] Complex function theory and numerical analysis [J].

Takahasi, H .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2005, 41 (04) :979-988

[10]

Tanaka Ken'ichiro, 2007, Transactions of the Japan Society for Industrial and Applied Mathematics, V17, P73

← 1 2 →