Periodic Gaussian filter according to ISO 16610-21 for closed profiles

It is well known that the Gaussian filter according to ISO 16610, part 21 has nice metrological properties but also has some restrictions. The evaluable measuring length of open profiles is shortened by so-called filter running-in and running-out lengths which are a factor of the width of the Gaussian weighting function. ISO 16610-21 suggests a simplistic transfer of filtering of open profiles to filtering of closed profiles (e.g. roundness measurements). And this leads, due to the running-in and running-out lengths, to an unnecessary restriction. Because in case of a closed profile, it has to be taken into consideration that the profile can be extended infinitely and thus any measuring length of an equivalent open profile can be reproduced. Hence, as this paper shows, the measuring length for closed profiles can be arbitrary for any given width of the Gaussian weighting function.