Estimation of mean squared errors of non-binary A/D-encoders through Fredholm determinants of piecewise-linear transformations

Abstract

Using the theory of Fredholm determinants of Perron-Frobenius operators of piecewise-linear maps, we derive a mathematically rigorous upper bounds of mean squared errors of analog-to-digital converters based on β-expansions. We also explain the technique of calculating the upper bound numerically by means of the numerical verification method.