One-Dimensional Optimal Analog to Digital Converter Design

TL;DR

This paper presents a method for designing optimal one-dimensional analog-to-digital converters (ADCs) using dynamic programming, resulting in a structure similar to classical Delta-Sigma Modulators with optimal quantization.

Contribution

It introduces an algorithm that exploits the problem's structure to analytically find the optimal ADC design and certifies its optimality.

Findings

The algorithm finds the optimal value function exactly.

The designed ADC has a Delta-Sigma Modulator structure.

Optimal quantization step spacing is achieved.

Abstract

The paper deals with the task of optimal design of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal discrete-time dynamical system with outputs taking values in a finite set, and its performance is defined as the worst-case average intensity of the filtered input matching error. The design task can be viewed as that of optimal quantized decision making in a system, with the objective being to optimize the performance measure. An algorithm is proposed for designing optimal ADCs and certifying their optimality. The algorithm is based on exploiting a special structure in the underlying dynamic program, which makes it possible to find the optimal value function, and hence the optimal quantization law exactly and analytically. Moreover, the designed ADC is shown to have the classical Delta-Sigma Modulator (DSM) structure with optimal quantization step spacing.