The analysis of the performance of a delta modulator with a Wiener process input is considered. The mean and the variance of the steady-state squared error are derived. In addition, the mean of the steady-state error of order four is calculated. It is shown that the behavior of all these moments as functions of the step size Δ and the sampling intervalTis similar: for each fixed Δ, the moments are monotonically increasing inT. More important, for each fixedT, there exists an optimal step size Δoptwhich minimizes each of these moments. It is shown that Δoptis a multiple ofT^{1/2}and that the corresponding minimum value of the moments is a multiple of eitherTor T², depending on the order of the moment.