A transmission characteristic of the robust Gaussian filter by using fast M-Estimation method

Gaussian filter to extract the roughness profile from a primary profile suffers strongly from the outliers mingled in the data. To solve this problem, several schemes of robust Gaussian filter have been proposed. However there are several fatal problems that a mean line determined with respect to the measurement data containing no outliers is not coincident with the mean line of the Gaussian filter output. To solve this problem, we have been proposed the robust Gaussian filter by using the fast M-Estimation method. This proposed method could provide completely the same results of the original Gaussian filter method. However, it is not confirmed whether a transmission characteristic of this method is corresponding to the transmission characteristic of the Gaussian filter. Therefore, this method cannot be applied to the real applications for the measurement of roughness profile where the transmission characteristic of Gaussian filter is strictly treated. In this paper, we confirm that the transmission characteristic of this method is corresponding to the transmission characteristic of the Gaussian filter.