Time-domain properties of instantaneous uniform quantization

Based on many examples and counterexamples, time-domain properties of instantaneous uniform quantization (IUQ) are analyzed. It is concluded that the most important attributes of an IUQ are the equivalence of its (input) quantization intervals and the uniqueness of their representation. Several equivalent definitions of IUQ independent of their specific mathematical representation are proposed. Several important properties of IUQ are shown to exist regardless of their mathematical description. Two models, direct and additive, of IUQ have been studied. A direct quantization is a four-parameter (quantization step, mode, offset, and gain) function. For the additive model, a unity gain had to be assumed. The utility of this material has been illustrated by an example