带有给定分布密度的三维相关随机表面模拟

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王泽华

 （青岛科技大学 数理学院，山东 青岛 266061）

 摘要： 为研究非高斯相关随机表面生成散斑场的特性，介绍了一种模拟具有给定分布密度的三维相关随机表面的方法。用高斯白噪声通过FIR指数滤波器模拟产生符合高斯分布的相关随机表面；并引入累积分布函数，将高斯随机表面转化为均匀分布的随机表面，在逆累积分布函数的作用下将均匀分布随机面转化为给定分布密度的相关随机表面，并对拟合度误差和相关长度误差做了简单估计。结果表明，所产生的相关随机表面能够很好的拟合规定的理论分布密度；当设定的相关长度较小时，模拟表面的实际相关长度能够较好的符合要求，但对于大的相关长度，要谨慎选择生成的相关随机表面。

 关键词： 相关随机表面；FIR指数滤波器；累积分布函数；分布密度函数；拟合度；相关长度

 中图分类号： O 431 文献标志码： A

 收稿日期： 20130628

作者简介： 王泽华(1972—)，男，副教授.

 Simulation of 3D CorrelationRandomSurface with Given PDF

 WANG Zehua

 (CollegeofMathematicsand Physics,QingdaoUniversityof Science and Technology,Qingdao266041,China)

 Abstract: Aimed at investigating the characterization of speckle field generated by nongauss correlationrandomsurface, a computer simulation method to generate 3D correlation random surface with a PDF is proposed. First, a gauss correlationrandomsurface is generated by convolution a gauss whitenoise and a exponential FIR. Next, CDF maps the gauss correlationrandomsurface to a uniform distribution correlationrandomsurface, which is mapped to a correlationrandomsurface with a given PDF by inverse CDF. The errors of PDF curve fitting degree and correlation length is estimated. The result show the PDF curve of the generated correlationrandomsurface fits the theoretical PDF curve. The error between the given correlation length and the correlation length of the simulation surface is tiny if the given correlation is small and vice verse. When a big correlation length is given, the choice of simulation surface generated by this method must be carefully.

 Key words: correlation random surface; exponential FIR; CDF; PDF; fitting degree; correlation length