A deterministic study of delta modulation

Delta modulation has often been viewed as a type of PCM and has been analyzed by probabilistic methods. This paper views delta modulation as a hybrid PDM/PAM system. A nonlinear feedback model is constructed and subjected to digital computation on an IBM 650. Computation is enabled by trapezoidal convolution, an approximate -transform method for solving dynamical systems. Responses to various steps and ramp inputs for unity and nonunity feedback are considered. Dead space is also introduced into the nonlinearity in the forward link. A series of computer runs is condensed and observations are reported. A typical observation is that a trade-off exists between average error and noise and that both may not be minimized by any one of two versions of the delta modulator.