Analog to Digital Conversion in Physical Measurements

There exist measuring devices where an analog input is converted into a digital output. Such converters can have a nonlinear internal dynamics. We show how measurements with such converting devices can be understood using concepts from symbolic dynamics. Our approach is based on a nonlinear one-to-one mapping between the analog input and the digital output of the device. We analyze the Bernoulli shift and the tent map which are realized in specific analog/digital converters. Furthermore, we discuss the sources of errors that are inevitable in physical realizations of such systems and suggest methods for error reduction.