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.