工程表面分数阶样条滤波分析法  

Analysis Engineering Surface with Fractional Spline Filter

作　　者：张浩[1] 袁怡宝[1] 朴伟英[1] 张峰[1] 

机构地区：[1]哈尔滨工业大学电气工程与自动化学院,黑龙江哈尔滨150001

出　　处：《计量学报》2011年第1期1-6,共6页Acta Metrologica Sinica

基　　金：教育部留学回国人员科研基金项目（AEBQ24403704）

摘　　要：将分数阶样条滤波器作为表面轮廓滤波器以获取表面中线。首先将分数阶样条函数与变分公式相结合，推导出分数阶样条滤波器系统函数。分析了该滤波器的幅度传输特性，其具有截止幅度可调性质。当样条阶次逐渐升高时，截止特性可接近理想低通滤波器，而当阶次r=1．51时，截止特性又可逼近于高斯滤波器，该特性极大地方便了样条滤波器的使用。给出了分数阶样条滤波器的快速FFT算法，由于该滤波算法只涉及频域内乘积，且运算数量有限，所以计算效率很高。最后对FFT算法产生边缘效应的原因进行了分析，并对边缘效应进行了修正。实验结果表明：该滤波器算法不但具有灵活可调的截止特性，而且计算速度快，在通用计算机上完成一次11200点表面中线的提取只需4ms，同时有效抑制了样条滤波器的边缘效应。Fractional spline theory is proposed as a new profile filter for mean line extraction. First, the fractional spline filter is derived by combining fractional spline function with variational principle. The amplitude transmission characteristics of this filter show its adjustability of cut-off characteristics, which can approach ideal low pass filter when the order of spline increases enough, and approximate to Gaussian filter when order is defined 1.51. A fast FFT algorithm is given to perform fractional spline filter. Provided with the limited number of multiplication operation during frequency domain, the computation is testified efficient. Finally, the reasons of end distortion during this algorithm are discussed, and this distortion called end effect is remedied. Experimental results indicate this filter algorithm preserves not only adjustable cut-off characteristics, but also fast computation speed. Based 6n this filter, once extraction for mean line of 11200 data points only costs 4 ms on general computer. In addition, the end effect existing in spline filter is alleviated by this algorithm availably.

关 键 词：计量学 分数阶样条滤波器 幅度传输特性 表面 傅里叶变换 

分 类 号：TB92[一般工业技术—计量学]