On the Need of Analog Signals and Systems for Digital-Twin Representations

We consider the task of converting different digital descriptions of analog bandlimited signals and systems into each other, with a rigorous application of mathematical computability theory. Albeit very fundamental, the problem ap-pears in the scope of digital twinning , an emerging concept in the field of digital processing of analog information that is regularly mentioned as one of the key enablers for next-generation cyber-physical systems and their areas of application. In this context, we prove that essential quantities such as the peak-to-average power ratio and the bounded-input/bounded-output norm, which determine the behavior of the real-world analog system, cannot generally be determined from the system’s digital twin, depending on which of the above-mentioned descriptions is chosen. As a main result, we characterize the algorithmic strength of Shannon’s sampling type representation as digital twin implementation and also introduce a new digital twin implementation of analog signals and systems. We show there exist two digital descriptions, both of which uniquely characterize a certain analog system, such that one description can be algorithmically converted into the other, but not vice versa.