高阶取样定理*
Samplin9 Formulae of Higher Order
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摘要: 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间隔作微小牺牲的前提下,得出了收敛速度比Shannon取样公式快得多的三阶、四阶和五阶的取样公式[1].本文在彭先生工作的基础上,给出了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。Abstract: Shannon sampling theorem is the basic theorem in signal reconstruction based on discrete sampling values in communication theory. The convergence rate of this formula,however,is very slow. Professor Pen Rui-reng. after some slight compromiseon 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 computer proves that it converges much faster than the Shannon formula. This paper gives a general method to comstruct a higher order sampling formula.
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Key words:
- band-limited /
- sampling /
- Nyquist frequency
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[1] 彭瑞仁,信息技术中的数据玉缩—快速取样定理,上海工业大学学报,15(4)(1994). [2] 李世雄,Radon变换的抽样取值与小波,地球物理学报,36(2)(1993). [3] Jerry.A.J.,The Shannon Sampling Theorem,proc.IEEE,65(1977). [4] Opp}nhoim,A,V.,Signais and Systems,Preutiy-HaII,Inc.(1983). -
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