表面测量中高斯滤波器的B样条函数实现方法

提出一种新的高斯滤波器B样条函数实现方法。在B样条函数理论基础上,通过对变分原则引入约束条件的方法,并结合小尺度高斯滤波器级联的特性,得出了高斯滤波器的逼近滤波器。其与高斯滤波器的最大幅度偏差小于1%,并且也具有零相移的特性。在相应的滤波算法中,包括了一级零相移滤波和一级加权滤波,只进行二次循环,算法结构简单,计算效率高。对实际表面测量数据进行应用试验,能够满足高斯滤波器实现方法高精度、高效率的要求。     

减小圆度测量中2RC滤波传输偏差的新方法

用双线性变换法和冲激响应不变法设计的逼近2RC滤波幅度特性的相位校正的数字滤波算法,其偏差大小相近,符号相反.因此两种滤波算法的线性组合极大地减小了逼近2RC滤波理论幅度特性的偏差,从而提高了圆度测量的滤波精度.     

三维表面测量中的高斯滤波快速算法

基于中心极限定理提出了一个高斯滤波器逼近模型,并利用冲激响应不变法设计了数字高斯滤波器.通过级联方法,该滤波器的幅度传输特性偏差可控制在(-0.28％～+1.14％)以内,扩展为二维高斯滤波器,其三维幅度传输特性偏差可控制在(-0.42％～+1.12％)以内.该滤波器采用递归实现算法,算法简便,易于实现.在递归算法的基...     

三角窗逼近法实现高斯滤波器

在中心极限定理和逼近理论的基础上,提出了一种用三角滤波器的级联来实现高斯滤波器的新方法.根据三角窗函数的对称性和三角滤波器的递归性,给出了高斯滤波器的实用逼近算法.实验表明,与传统的高斯滤波方法相比,新方法算法简单,计算效率高,且易于实现.     

一种新型稳健样条轮廓滤波器

在表面计量学中,通常利用轮廓滤波器提取轮廓中线作为表面评定的基准线。由于传统轮廓滤波器极易受到划痕和深谷等奇异信号影响而产生失真甚至错误的中线,为了增强其稳健性并保证评定精度,国际标准中给出了两种替代滤波器,即稳健型样条滤波器和高斯回归滤波器。然而,这两种滤波器的构造原理和实现算法迥异,其滤波特性差异较大,从而导致对同一表面具有不同的评定结果。为解决这一问题,提出将M估计权函数与样条滤波器相结合构造了一种新型稳健样条滤波器。该滤波器不但具有更强的抗差能力,其计算效率也远高于国际标准推荐的稳健滤波器。更重要的是,大量实验表明,其滤波特性与高斯回归滤波器接近,该滤波器的应用有助于表面评定标准的传递和测量结果比对。     

国标圆度仪数字滤波器传输特性逼近方法的研究

国标ＧＢ７２３５－８７给出了圆度仪滤波器的传输特性曲线,由于量值的传递关系,在圆度测量数据预处理时,要求所设计的滤波器的幅度传输特性曲线严格逼近国标给定曲线。本文提出了修正载止频率的Ｂｕｔｔｅｒｗｏｒｔｈ混合滤波设计法,使得滤波器在截止频率处的传输误差为零,其它频段对国标特性曲线的最大逼近误差为２％。该滤波器已应用于ＨＩＴ－ＴＡＮＬＹ大型圆柱度仪误差分离系统中,成功地复现了国标滤波器幅度传输特性曲     

线性相位递归数字滤波器设计

本文讨论了运用线性规划设计递归数字滤波器。在求解滤波器稳定性问题时,通常是利用试探法或者把充分的但不是必要的线性稳定性约束条件加到滤波器的逼近方法中。本文提出了一种求解这类稳定性问题的不同方法。作为一个例子,在新近的 Chottera 和 Julien 方法中,采用了这一稳定性的新方法同时对给定的幅度和线性相位特性进行逼近,我们发现这种方法将使计算时间和数据处理量大幅度减少。文中通过几个设计例子的比较,说明了改善程度。     

样条滤波器算法的实现

在表面粗糙度测量中,样条滤波器比之前的2RC滤波器和高斯滤波器有更好的滤波效果,但是样条滤波器的截止波长λ,没有确定的定义,这使得样条滤波器的应用受到了限制.本文通过大量的计算,进行数据拟和得到了样条滤波器截止波长的拟合公式,通过该公式可以直接计算出p参数,它使得滤波器在截止波长处的传输特性为50%,而且其相关系数达到了1,非常接近实际的计算值.     

椭圆滤波器边带优化设计方法研究

给出了椭圆函数滤波器边带特性优化设计的一种新方法。该方法把椭圆函数滤波器的边带选择性作为一个设计参数进行优化处理,充分利用函数逼近阶数的计算余量,通过相应的算法调整归一化的阻带角频率使边带选择特性最大化,可以在不增加阶数的前提下获得更好的衰减特性,有效地减小过渡带宽。文中给出了计算方法和实例分析。     

小波滤波器的开关电流电路设计与实现

本文首次提出基于开关电流技术的小波滤波器的设计与实现。小波滤波器在模拟VLSI小波变换的实现中起着关键的作用,Padé逼近是一种有效的有理逼近。采用高斯函数一阶导数作为基本小波,用Padé变换获得其有理分式逼近,利用开关电流技术实现小波滤波器可获得小波变换所需的基本小波及其膨胀小波。仿真结果验证了小波滤波器的良好特性。     

Optimal and near-optimal filters in high-resolution electron microscopy

Two filters for improving the visibility of crystalline material in the presence of amorphous surface contamination layers in high-resolution electron microscope images can be constructed automatically from the information present in the Fourier transform of the recorded image. The recorded signal is considered in the first approximation to be the sum of two signals which are uncorrelated in the frequency domain. By estimating the power spectrum of the signal from the amorphous layer, an optimized estimate for the desired signal is given by the Wiener filter. A second filter which uses the estimated amplitude of the amorphous signal to subtract out a background can be shown to be related to the Wiener filter. The two filters are applied to an experimental image of zeolite and the effects of the two filters are compared.     

The filtering method to calculate the transmission characteristics of the low-pass filters using actual measurement data

The Gaussian filter and spline filter are low-pass filters used in surface roughness estimation methods, and their transmission characteristics are well known. However, the transmission characteristics of the Gaussian filter and spline filter used at actual sites may not be in agreement with their theoretical characteristics. Generally, the spline filter is used with an open profile. Although the transmission characteristics of the periodic spline filter are well known, these transmission characteristics are not those of a nonperiodic spline filter used with an open profile. In the case of a Gaussian filter, the filter width of the theoretical transmission characteristics is ∞. However, a Gaussian filter of filter width λ_c is used at actual sites. This fact is a major problem. To solve this problem, it is necessary that the transmission characteristics of a low-pass filter are obtained from actual measurement data and the filter output. However, it is not possible to calculate the transmission characteristics from actual measurement data owing to the end effect and the discontinuity at each end of the data, etc. In this paper, we propose a new method for exactly calculating the transmission characteristics of a low-pass filter. This method involves the process in which the open profile is considered as a closed profile by repeating it periodically. The transmission characteristics of a nonperiodic spline filter and a Gaussian filter (filter width λ_c) used at actual sites were confirmed by the proposed method. The transmission characteristics of the Gaussian filter of filter width λ_c were almost the same as the theoretical characteristics. However, the transmission characteristics of the nonperiodic spline filter were considerably different from those of a periodic spline filter with well-known characteristics. Moreover, the transmission characteristics of the nonperiodic spline filter were found not to be unique.     

B样条滤波器建立表面轮廓中线的方法

根据离散B样条函数的Z域表达式，B样条空间中对信号的拟合和分解可以表示成FIR滤波器和IIR滤波器的滤波过程，再结合变分原则，构建了表面粗糙度测量中用于确定中线的B样条滤波器。将零相移滤波技术应用到B样条滤波器的实现中，得到了相应的差分方程。对一实际工件表面轮廓进行了实验，验证了该方法的可行性，该滤波器同样具有零相移的特性，与其它方法相比，其具有计算效率高的优点。     

High-order spline filter: Design and application to surface metrology

The differences between the transmission characteristics of the standard cubic spline filter and the Gaussian filter lead to different evaluation results even for the same profile. There is indeed an adverse impact on the comparison of measurement results and the applications of the related international standards. A novel high-order spline filter is proposed to resolve this practical problem of approximating the Gaussian filtering characteristic. The design of the new filter is based on an improved variational approach by adding the high order derivative terms to the bending energy part whose structural parameters are determined by the aid of the universal Taylor series, so as to realize the convergence to the function of the Gaussian filter. In addition, a cascade algorithm in terms of the low-order filters is also developed in order to ensure stable performance of the high-order filter. Its effectiveness and application were verified by the experiments.     

A universal spline filter for surface metrology

In this study, a novel fractional spline filter is proposed for surface metrology. The filter combines arbitrary order fractional spline function with variational principle, and is endowed with an adjustability of transition characteristic. If the order is high enough, the fractional spline filter can obtain more step-edge-like cut-off characteristic of the low-pass filter, and it can also realize the transmission characteristic of the Gaussian filter with high accuracy if the order equals to two. In addition, if the approximation parameter is set to zero, this filter will be simplified to a form of ordinary spline filter. Therefore, this fractional spline filter is called the universal spline filter. In order to reduce the computation time, the universal spline filter is calculated by a fast Fourier transform (FFT) algorithm. Furthermore, for practical use, an improved method prior to the FFT algorithm is proposed to suppress the end effect. Finally, the efficiency of the whole algorithm in comparison with the ordinary spline filter is demonstrated by the experiments, and it is also shown that the universal spline filter is able to alleviate the end effect significantly.     

随动磨削曲轴表面异常轮廓误差去除方法

在高精度随动曲轴磨床中,为控制曲轴加工轮廓误差常采用预补偿的方法,如果测量时工件上有磨屑、毛刺等干扰将在测量结果中引入明显的异常轮廓,采用传统的高斯滤波器对数据进行处理将极大地影响轮廓误差的补偿精度,甚至导致废品出现。针对这一问题,给出了适用于闭轮廓的高斯滤波器、Rk滤波器和鲁棒高斯回归滤波器的理论模型。分别应用3种滤波器,对比分析结果可知,鲁棒高斯回归滤波器去除异常轮廓误差效果最理想,并通过人为改变异常轮廓的尺度,进一步验证鲁棒高斯回归滤波器的适应性和可靠性。该滤波方法集成到随动曲轴磨床软件中,实现异常轮廓的自动去除,提高了补偿效率,有效保证了曲轴磨削轮廓的误差精度。     

An in-line digital filtering algorithm for surface roughness profiles

The authors develop a fast algorithm for low- and high-pass Gaussian digital filters, executed while one discrete datum of a traced profile is sampled. In this report, the 8-step, modified running–box-function filter is presented. The transmission characteristics of this new filter are very close to those of the Gaussian digital filter given in ISO 468-1982. In addition, the conditions for using this filter are given for practical use.