Abstract: n this paper, the derivative process of the trapezoidal shaping impulse response function with the inverse z transform method was introduced, and its correctness was verified when the exponential nuclear signal by software was inputted. When Gaussian white noise of different standard deviations and exponential signal are inputted together, the standard deviation ratio of output signal and Gaussian white noise is 0.447. Finally, the correctness of the theoretical derivation and result was verified when the actual nuclear signal was trapezoidally shaped which is generated from digital nuclear signal acquisition platform.