分数布朗运动, 离散傅里叶变换, 分形轮廓, 表征参数

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.

fractional Brownian motion, discrete Fourier transform, fractal profile, characteristic parameter