Abstract: This paper discusses noise-improved signal correlation in the autoregressive model of order one [AR（1）] for three representative noises.When the input is subthreshold or partly subthreshold，the correlation coefficient increases firstly and then decreases as the noise intensity increases，some noise can improve signal correlation，Stochastic Resonance（SR） exists.The efficacy of SR decreases and the optimal noise becomes large as the threshold increases.The efficacy of SR also decreases as the impulsion of the noise Probability Density Function（PDF） around the zero mean becomes higher and the tail in the PDF becomes heavier.There is a range of the noise intensity，the correlation coefficient between the input and the output signals is greater than that of the input signal and the noisy signal，the output signal is more similar with the input signal than the noisy signal in AR（1）.These results show that noise can improve signal correlation through the discrete-time system，SR exists and SR is of certain robustness for noise.These results also extend SR to be applied in digital signal processing.

Key words: correlation coefficient, stochastic resonance, discrete-time system

摘要： 讨论一阶自回归模型中三种典型噪声改善信号的相关性问题。当输入信号在阈下或部分在阈下时，随着噪声强度的增加，输出信号与输入信号的相关系数先递增后递减，适量的噪声改善了信号的相关性，随机谐振现象存在。随着阈值的增加，随机谐振功效降低、最佳噪声值变大；随着噪声密度函数在零均值周边脉冲值变大和拖尾变厚，随机谐振功效也降低。存在一个噪声范围，其间输入信号与输出信号相关系数大于输入信号与噪声信号相关系数，一阶自回归模型中输出信号比噪声信号与输入信号更相关。这些结果说明在离散时间系统中噪声改善信号的相关性，随机谐振现象存在，且随机谐振对噪声具有鲁棒性。这些结果也拓广了随机谐振在数字信号处理中的应用。

关键词: 相关系数, 随机谐振, 离散时间系统