A deterministic approach to variable-step delta modulation

A study is described of delta modulators where the quantizing parameter
\Delta
is a function of a finite number of previously emitted bits. Sufficient conditions are obtained for bounding the steady-state quantization error by the current value of
\Delta
under the assumption that input signals are limited both in amplitude and frequency. The nonlinear problem associated with determining a bounding rule is partitioned into a set of problems amenable to linear programming techniques. Results of the analysis are compared with those obtained from a stochastic approximation program.