As the key link in the field of signal processing

the integrator is widely used in measurement in power system and control engineering. Generally

research on the digital integrator is based on traditional Newton Cotes algorithm

the high frequency response of low order Cotes formula is usually poor

and the design of the transfer function introduced by high order of the formula is too complex. Based on a study of error between the composite Cotes transmission function and ideal integration

the output signal which are weighted by Romberg algorithm at the same algorithm order before and after integrator sampling frequency are doubled

then the accuracy of digital integrator is improved and the composite is lower. The digital integrator designed with better transient and steady performance has an accuracy of 0. 01% as verified by simulation and test. This work is supported by National Natural Science Foundation of China(No. 51507091)and Hubei Provincial Natural Science Foundation of China(No. 2015CFB219).