On the Estimation of Quantizer Reconstruction Levels

We consider the problem of estimating the optimal reconstruction levels of a fixed quantizer, such as the amplitude quantization part of an analog-to-digital converter. A probabilistic transfer function model is applied for the quantizer. Two different assumptions are made for the transfer function, and an estimator based on order statistics is applied. The estimator turns out to give better results in terms of mean square error than the commonly applied sample mean. The Cramer-Rao lower bound for the estimation problem is also considered, and simulation results indicate that the derived estimator is asymptotically efficient