Statistical efficiency of the ADC sinewave histogram test

Abstract

This paper presents an analysis of the statistical efficiency of the sinewave histogram test used for estimating the unknown transition levels of an analog-to-digital converter. Accordingly, at first, a closed-form determination of the Cramer-Rao bound is derived under the assumption of a noiseless stimulus signal. Both unbiased and biased versions of the bound are described in order to account for the eventual bias introduced by commonly employed estimators. Then, additive Gaussian noise is assumed, and comments are made about its effects on the maximum achievable accuracy.