A smoothing algorithm for energy spectrum based on differential nonlinearity(DNL) error elimination with total counts conservation for high-energy particle detector systems is presented. It is physics based and is only determined by the DNL error of analog-to-digital converter device itself. From the experimental results, this algorithm slightly improves both noise performance and energy resolution, while greatly reduces the testing errors by almost a half compared to their original values. In addition, the reduced-x^2 statistic for evaluating the Gaussian fitting goodness is significantly reduced by almost two orders after smoothing. As a typical verification example,this algorithm is successfully applied in the ground calibration of the Low Energy X-ray Instrument onboard the Hard X-ray Modulation Telescope(HXMT-LE) satellite,lending it a powerful, nondestructive and low-cost tool for both calibration and data processing for high-energy particle detector systems.
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