Criteria for Obreshkov-like numerical integrators to be used as numerical differentiators are proposed in this paper. The coefficients of a numerical integrator for the highest order derivative turn out to determine its suitability and potential hazards such as numerical oscillation and bias. The suitability of some existing Obreshkov-like numerical integrators is examined. It is revealed that the notorious numerical oscillations induced by the implicit trapezoidal method cannot always be eliminated by using the backward Euler method for a few time steps. Guided by the proposed criteria, a frequency response optimized integrator considering second order derivative is put forward which is suitable to be used as a numerical differentiator. Theoretical observations are verified in time domain via case studies.

翻译：本文提议了Obreshkov类数字集成器用作数字差异器的标准。对于最高顺序衍生物,数字集成器的系数可以用来确定其是否合适和潜在危险,如数字振荡和偏差。一些现有的Obreshkov类数字集成器的适宜性得到了审查。据透露,通过使用后向电极方法采取若干步骤,无法总是消除隐含的诱杀性诱杀性方法引起的臭名昭著的数字振动。在拟议标准的指导下,提出了一个考虑到第二顺序衍生物的频率优化集成器,适合用作数字差异器。通过案例研究在时间域核查理论观察。