ha o - dy n / 99 01 02 8 v 1 2 6 Ja n 19 99 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. Progress in physics is based on the intimate relationship between experiment and theory. Experiments involve measurements in which the precision of the measured quantities depends essentially on the particular characteristics of the measuring devices. Often this process of measurement involves a conversion of the analog measured quantity into a digital number by means of a converter. For such analog/digital converters, there exists an internal relationship between the quantity to be measured (analog input), and the result of the measurement process (digital output). We assume that the conversion of the analog signal into a digital number is the sole process in such converters 1