Abstract: In order to deal with the frequently encountered non-stationary random signals in signal processing, they can be divided into sub-stationary random signals, and autocorrelation function can be used to reflect the essential characteristics of sub-stationary signals. The computation of piecewise stationary stochastic process autocorrelation function was discussed. In order to reduce the amount of calculation and errors of the existing function models, a new model to approximate autocorrelation function of piecewise stationary stochastic process was proposed in this paper. The computer simulation shows that the model can effectively approximate autocorrelation function. The computing speed is faster, and the errors are much fewer and smoother. Applying the model to the restoration of blurred digital images, a very good restoration effect can be got.

Key words: piecewise stationary stochastic process, Poisson process, Auto Regress (AR) model, autocorrelation function

摘要： 为处理信号处理过程中经常遇到非平稳随机信号，可以将其划分为分段平稳随机信号，而自相关函数则可以用来反映分段平稳信号的本质特征。分析了分段平稳随机过程自相关函数的计算，针对传统的函数逼近模型计算量较大、误差较高等缺点，提出一种新的自相关函数的逼近模型，给出分段平稳随机信号的自相关函数的近似表达式，并利用牛顿迭代法进行优化计算。仿真实验证明模型计算速度快，具有较好的逼近效果，误差也明显降低，而且变化相对平缓。将其应用到数字图像信号进行模糊图像恢复，得到了很好的恢复效果。

关键词: 分段平稳随机过程, 泊松过程, 自回归模型, 自相关函数