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

• Transmission characteristics of Gaussian filter and spline filter may differ from used at actual sites.
• In case of SF, theoretical characteristics are periodic SF's. Nonperiodic SF's are unknown. In case of GF, filter width is different.
• We solve problem that it was impossible to calculate the transmission characteristics that is used at actual sites.
• Transmission characteristics of the GF of filter width λc were almost the same as theoretical.
• Transmission characteristics of the nonperiodic SF were different from theoretical and not to be unique.

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 λc 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 λc) used at actual sites were confirmed by the proposed method. The transmission characteristics of the Gaussian filter of filter width λc 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.