  This paper proposes a differentiator for sampled signals with bounded noise
and bounded second derivative. It is based on a linear program derived from the
available sample information and requires no further tuning beyond the noise
and derivative bounds. A tight bound on the worst-case accuracy, i.e., the
worst-case differentiation error, is derived, which is the best among all
causal differentiators and is moreover shown to be obtained after a fixed
number of sampling steps. Comparisons with the accuracy of existing high-gain
and sliding-mode differentiators illustrate the obtained results.
