基于离散傅里叶变换的分形粗糙表面轮廓合成与研究

Study of Synthesized Fractal Surface's Profiles Based on Discrete Fourier Transform

针对使用离散傅里叶变换合成的分形粗糙表面轮廓,分别研究轮廓的分形参数(分形维数D、尺度系数C)与传统表征参数的联系,分形参数对轮廓空域几何形貌的影响以及分形参数对轮廓滤波的影响。结果表明,若假设分形轮廓的功率谱密度函数严格满足幂律关系,则可由Parseval定理获得轮廓分形参数与其方均根偏差Rq的定量关系但此时,轮廓的其余传统表征参数为随机值,且相互之间线性无关;分形维数D影响轮廓高低频成分的能量比随着D的增加,轮廓高频成分的能量增加,轮廓空域几何形貌显得凹凸不平;分形维数D相同时,尺度系数C越大,轮廓的方均根偏差越大;在为获得光滑分形轮廓进行滤波时,分形维数D较小的轮廓,可以保留更多的能量。

To the fractal profiles synthesized by discrete Fourier transform,the relationship between fractal parameters（fractal dimension D,scale factor C） and traditional parameters,the influence of fractal parameters on the geometric shape of profiles,and the influence of fractal parameters on filtering are studied respectively.It is found that if the power spectrum of a profile is assumed to fit the power law strictly,a quantitative relationship between fractal parameters and root mean square deviation can be established by Parseval theorem,but the rest of traditional parameters are still random and not linear related.Fractal dimension D influences the energy ratio between high frequency components and low frequency components of a profile.D increasing,the high frequency components of a profile are increased,which makes the geometric shape of a profile appear rougher.With the same fractal dimension,if the scale factor is larger,the root mean square deviation is larger.When a fractal profile is filtered to be smooth,more energy can be preserved in a profile with smaller D.