高阶取样定理

Ｓｈａｎｎｏｎ取样定理是通讯理论中根据离散取样值重建信号的一个最基本定理，彭瑞仁先生在对取样问题作微小牺牲的前提下，得出了收敛速度比Ｓｈａｎｎｏｎ取样公式快得多三阶，四阶和五阶的取样公式。本文在彭先生工作的基础上，给出构造高阶取样公式的一般方法以及一种Ｎ阶取样公式的简单形式。

Samplin9 Formulae of Higher Order

Shannon smapling theorem is the basic theorem in signal reconstruction based on discrete sampling values in comunication theory. The convergence rate of this formula,however is very slow. Professor Pen Rui-reng, after some slight com-promise on sampling rate, has come to the 3rd order,the 4th order and the 5th order sampling formulae. The calculation of the third order formula on the com-puter proves that it converges much faster than the Shannon formula. This paper gives a general method to construct a higher order sampling formula.