## 留言板

 引用本文: 杨守志, 程正兴, 唐远炎. 二维连续信号的近似采样定理[J]. 应用数学和力学, 2003, 24(11): 1197-1203.
YANG Shou-zhi, CHENG Zheng-xing, TANG Yuan-yan. Approximate Sampling Theorem for Bivariate Continuous Function[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1197-1203.
 Citation: YANG Shou-zhi, CHENG Zheng-xing, TANG Yuan-yan. Approximate Sampling Theorem for Bivariate Continuous Function[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1197-1203.

## 二维连续信号的近似采样定理

###### 作者简介:杨守志(1963- ),男,河南罗山人,副教授,博士(E-mail:yangshouzhi@263.net).
• 中图分类号: O174.42

## Approximate Sampling Theorem for Bivariate Continuous Function

• 摘要: 利用加细方程的面具,给出该方程的一个近似解,并根据这个近似解构造出二维连续信号的近似采样定理.其近似采样函数是所求加细方程的近似解,它是由加细方程的面具唯一确定的逐段线性函数,且有显示的计算公式.因此可以根据需要选择加细方程的面具,从而达到控制近似采样函数的衰减速度.
•  [1] Shannon C E.A mathematical theory of communication[J].Bdll System Tech J,1948,27(3):379-423. [2] Walter G G.A sampling theory for wavelet subspace[J].IEEE Trans Inform Theory,1992,38(2):881-884. [3] 郭田德,高自友,吴士泉.基于双尺度方程近似解的适合任何连续信号的近似采样定理[J].系统科学与数学,2001,21(1):64-71. [4] 杨守志,程正兴.有限区间小波子空间上的采样定理及H2(I)空间中函数的逼近表示[J].数学物理学报,2001,21(3):410-415. [5] Daubechies I,Lagarias J.Two-scale defference equation,I:Global regularity of soutions[J].SLLAM J Math Anal,1991,22(5):1388-1410. [6] Daubechies I,Lagarias J.Twoscale difference equation-ⅡI:Local regularity,infinite products and fractals[J].SLAM J Math Anal,1991,22(4):1031-1079. [7] Lau K S,Wang J R.Characterization of solutions for two-scale dilation equations[J].SIAM J MathAnal,1995,25(4):1018-1046. [8] 程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,1998. [9] Berger M A,Wang Y.Multidimensional two-scale dilation equations[A].In:Chui C K,Ed.Wavelet:Atutorial in Theory and Applications[C].New York:Academic Press,1992,295-323. [10] HE Wen-jie,LAI Ming-jun.Examples of bivariae nonseparable compactly supported orthonormal continuons wavelets[J].IEEE Trans Inform Theory,2000,9(5):949-953.

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##### 出版历程
• 收稿日期:  2001-07-03
• 修回日期:  2003-06-17
• 刊出日期:  2003-11-15

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