The quantization precision is determined by the word-length of analog-to-digital converters. But by adding noise to the signal before quantization and averaging a set of quantization results
the quantization error can be reduced. A strictly mathematical analysis is given in this paper. The conditions for unbiased estimation and the minimum sampling number needed in averaging in order to reach a given quantization precision are given. Particularly
the performances using Gaussian noise and uniform distribution noise as the additional noise are analyzed and compared in detail.