New Results From a Mathematical Study of an Adaptive Quantizer
Debasis Mitra · Bell System Technical Journal · 1975
We consider a general class of multibit adaptive quantizers in which the quantizer function is modified at every sampling instant according to a recursive law with the transitions depending on the value of the quantizer output. We obtain a rather comprehensive set of basic properties of the device which explain the interrelationship of different aspects of the device behavior and their dependence on the parameters of the adaptation algorithm. For the quantitative analysis of the device, we give formulas and bounds for the mean time required for the quantizer function to adapt from an arbitrary initial state to the optimal. A feature new with this work is a unified treatment and a common body of results for quantizers with both bounded and unbounded range. This paper extends all the analytical results reported in an earlier paper, which dealt with a restricted class of quantizers having only four levels. We also present new results from a computational investigation on quantizers up to four bits (sixteen levels). These results indicate, for well-designed examples of the respective classes, the kinds of improvement in performance that can be expected in going from three-bit (eight-level) to four-bit quantizers and from uniform to nonuniform quantizers.