This paper presents a time discretization of therobust exact filtering differentiator, a sliding mode differentiatorcoupled to filter, which provides a suitable approximation to thederivatives of some noisy signals. This proposal takes advantageof the homogeneity of the differentiator, allowing the use ofsimilar techniques to those of the linear systems. As in the originalcase, the convergence robust exact filtering differentiator dependson the bound of a higher-order derivative; nevertheless, this newrealization can be implemented with or without the knowledge ofsuch constant. It is demonstrated that the system’s trajectoriesconverge to a neighborhood of the origin with a free-noise input.Finally, comparisons between the behavior of the differentiatorwith different design parameters are presented