International Symposium on Nonlinear Theory and Its Applications
Fredholm Determinants of Generalized $\beta$-Transformations and MSE Estimates of Corresponding AD-Converters
Katsutoshi Shinohara, Kenta Koayashi,
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We consider an Analog-to-Digital (AD) encoder defined by generalized $\beta$-transformation. Such encoders are called $\beta$-encoders. In this article, we show that the mean squared error of a $\beta$-encoder can be estimated by analyzing the zeros of the Fredholm determinant of the transformation. We give an example of a rigorous upper bound of the MSE by this technique, together with the numerical verification method.