二维连续信号的近似采样定理

基金项目: 河南省自然科学基金资助项目(984051900);河南省教委自然科学基金资助项目(98110015);河南省高校青年骨干教师基金资助项目

Approximate Sampling Theorem for Bivariate Continuous Function

1.
Department of Mathematics, Shantou University, Shantou, Guangdong 515063, P. R. China;
2.
Faculty of Scicnce, Xi'an Jiaotong University, Xi'an 710049, P. R. China;
3.
Department of Computer Science, Hongkong Baptist University, Kowlon Tong, Hong Kong, P. R.

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.
- 采样定理 /
- 二维连续信号 /
- 加细方程 /
- 加细方程的面具
Abstract: An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one's requirement, so that one may controll the decay speed of the approximate sampling function.
- approximate sampling theorem /
- bivariate continuous signal /
- refinement equation /
- mask of refinement equation

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