中文摘要：

基于分数布朗运动和离散傅里叶变换,针对分形轮廓样本的传统表征参数进行研究。研究结果表明：给定采样点数时,若假定分形轮廓的双对数功率谱为理想直线,那么可根据Parseval定理,获得轮廓均方根偏差与分形参数之间的定量关系;受相位谱随机性的影响,分形参数相同的分形轮廓样本,其支承率和算术平均偏差各不相同,但可通过多次随机试验,合成具有给定分形参数、均方根偏差、支承率以及算术平均偏差的分形轮廓。

英文摘要：

Based on fractional Brownian motions and discrete Fourier transform,the traditional characteristic parameters of fractal profiles were studied.It is found that with given sampling points,if the double logarithmic power spectrum of a fractal profile is assumed to be linear,the quantitative relationship between the profile＇s root mean square roughness and its fractal parameters can be established based on the theorem of Parseval.And because of the randomness of phase spectrum,the material ration and arithmetic average height of the profiles are still different even though the fractal parameters are the same.Through enough random experiments,a profile with given fractal parameters,root mean square roughness,bearing rate and arithmetic average height can be synthesized.