High-order spline filter and ideal low-pass filter at the limit of its order

We propose a method of obtaining a more vertical step-edge-like cut-off characteristic of a low-pass filter, in which a mean line for the roughness profile is extracted and the computation time is significantly reduced. In order to make the cut-off characteristic more step-edge-like, attention is focused on the relationship between the spline filter order and mean line smoothness, and the order is made larger. This filter, i.e., the high-order spline filter, has extremely low end effects because it is an extension of the spline filter. Raising the order of the high-order spline filter to ∞ can also realize an ideal low-pass filter that has a step-edge-shaped cut-off characteristic. In addition, in order to reduce computation time, the high-order spline filter is calculated in the frequency domain. When several thousand data points are used, the spline filter requires a maximum of 1 h, whereas using the proposed high-order spline filter allows computation to be completed in less than 1 s.