This report describes the results of a study of Statistical Delta Modulation (SDM), a new method of digital transmission of analog information [1]. In this method the system design is tailored to the statistical properties of the input data so as to provide analog reconstruction values with a minimum mean squared error. The method of system design is an iterative procedure in which conditional means are evaluated based upon actual input data. The report presents the theory of operation of the system and describes the results of a computer simulation in which such questions as the effects of sampling rate, channel noise, system memory, and mismatched input processes are discussed. At the present time only a brief comparison has been made with conventional techniques. It was found that at low sampling rates and for a particular non-Gaussian process, sampling rate reductions of 38 percent could be achieved relative to a conventional delta modulation system at the same SNR performance.