Given a known pulse superimposed on fluctuation noise having a known spectrum, we determine the frequency response of that linear device which would give the maximum value for the ratio between peak amplitude of the signal and the root-mean-square of the noise at the output. This result is applied to the case in which the fluctuation noise has a flat spectrum, and it is shown that in that case the optimal network is physically realizable if the pulse differs from zero for only a finite interval of time. The noise-suppressing efficiency of a conventional RC circuit is computed for pulse shapes of practical interest.