  This paper presents a time discretization of the robust exact filtering
differentiator, a sliding mode differentiator coupled to filter, which provides
a suitable approximation to the derivatives of some noisy signals. This
proposal takes advantage of the homogeneity of the differentiator, allowing the
use of similar techniques to those of the linear systems. As in the original
case, the convergence robust exact filtering differentiator depends on the
bound of a higher-order derivative; nevertheless, this new realization can be
implemented with or without the knowledge of such constant. It is demonstrated
that the system's trajectories converge to a neighborhood of the origin with a
free-noise input. Finally, comparisons between the behavior of the
differentiator with different design parameters are presented.
