Delta Modulation of the Wiener Process

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 interval is similar: for each fixed Δ, the moments are monotonically increasing in . More important, for each fixed , there exists an optimal step size Δoptwhich minimizes each of these moments. It is shown that Δoptis a multiple of and that the corresponding minimum value of the moments is a multiple of either or T², depending on the order of the moment.