  This paper deals with the design of discrete-time algorithms for the robust
filtering differentiator. Two discrete-time realizations of the filtering
differentiator are introduced. The first one, which is based on an exact
discretization of the continuous differentiator, is an explicit one, while the
second one is an implicit algorithm which enables to remove the numerical
chattering phenomenon and to preserve the estimation accuracy properties. Some
numerical comparisons between the proposed scheme and an existing discrete-time
algorithm show the interest of the proposed implicit discrete-time realization
of the filtering differentiator, especially when large sampling periods are
considered.
