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现有强震记录常规处理程序中采用的插值、积分、微分运算方法计算简单、省时，但在某些情况下、不能确保所要求的计算精度。针对这一问题，本文假定强震记录是理想的有限长记录并满足采样定理，在此基础上提出了对强震记录进行“精确”插值、积分和微分运算以及权函数的概念，井推导建立了相应的计算公式。理论和算例分析表明：（１）本文算法中使用的插值、积分和微分运算仪函数均具有不变和快速收敛的性质。（２）只需要少量的权系数，本文算法就能获得足够的计算精度；（３）选取足够多的权系数，本文算法能以任意精度逼近真实的精确解序列；（４）本文算法可以成为强震数据处理和相关结构动力分析的基础。
The interpolation, integral and differential calculation methods used in the routine processing of strong earthquake records are simple and time-saving, but in some cases, the required calculation precision can not be ensured. In this paper, we assume that strong earthquake records are ideal finite-length records and satisfy the sampling theorem. Based on this, the concepts of “accurate” interpolation, integral and differential operations and weight functions for strong earthquake records are proposed and well-established The corresponding calculation formula. Theoretical and example analysis shows that: (1) The interpolation, integral and differential operator functions used in this algorithm all have invariant and fast convergence properties. (2) Only a small number of weighting coefficients are needed, and the algorithm in this paper can get enough calculation precision. (3) Choosing a sufficient number of weight coefficients, the algorithm in this paper can approximate a real exact solution sequence with arbitrary precision. (4) Strong earthquake data processing and related structural dynamic analysis of the foundation.