A Study on Low-Pass Filter for Extracting Waviness Profile

—Substituting Gaussian Filter with Down-Sampling and G-Spline Filter—

Abstract

A method using a cubic spline filter is proposed to extract the waviness profile in the surface roughness measurement. An error in the waviness profile extracted by the spline filter is larger than one by a gaussian filter. Therefore, the spline filter hardly is used to extract the waviness profile. In this paper, cause of the error obtained by the spline filter was clarified using a B-spline basis function. The spline filter with a degree over the 11th order was required for practical use. This paper presents a new spline filter, called a G-spline filter, with a shape that is almost equal to the 11th order B-spline filter. By using the G-spline filter and down-sampling method, the waviness profile was accurately extracted at high speed than the usual Gaussian filter. The error obtained by the proposed method decreased to 1/10 of the error obtained by the conventional spline filter.