Separation of Quantization and Control in Optimal Analog to Digital Converters

TL;DR

This paper proves the optimality of a class of ADCs, similar to Delta-Sigma Modulators, by analyzing their worst-case error and demonstrating the separation of quantization and control under certain conditions.

Contribution

It provides an analytic expression for ADC performance and establishes the separation principle for quantization and control in this class of ADCs.

Findings

Optimality of certain ADCs with respect to worst-case error

Analytic expression for ADC performance

Separation of quantization and control proven under technical conditions

Abstract

In this paper we prove optimality of a certain class of Analog to Digital Converters (ADCs), which can be viewed as generalized Delta-Sigma Modulators (DSMs), with respect to a performance measure that can be characterized as the worst-case average intensity of the signal representation error. An analytic expression for the ADC performance is given. Furthermore, our result proves separation of quantization and control for this class of ADCs subject to some technical conditions.