获得快速取样定理的一个新方法

A New Method to Obtain High Speed Sampling Theorem

本文通过卷积来构造可表为初等函数的尺度函数，其形式简单．在光滑性、局部性等性质上优于其他构造方式所得结果，且其收敛于零的阶数可达到Ｏ（｜ｘ｜－Ｎ），此处Ｎ是任意正整数．从而由此尺度函数所建立的取样定理有更高的收敛速度．

his paper deals with the method of establishing new sampling theorem by using convolution and its theorem. We have improved the results obtained by Peng Ruiren in 1994. The new sampling theorem has a faster convergence rate and it is more useful than those developed by Peng Ruiren in a fast and exact algorithm.