Delta Modulation of the Wiener Process.
NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS
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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 delta and the sampling interval T is similar For each fixed delta, the moments are monotonically increasing in T. More important, for each fixed T, there exists an optimal step size delta opt which minimizes each of these moments. It is shown that delta opt is a multiple of square root of T and that corresponding minimum value of the moments is a multiple of either T or T squared, depending on the order of the moment.
- Statistics and Probability