Optimization of Digital-Twin Representations of Analog Signals and Systems

We consider the task of converting different digital descriptions of analog bandlimited signals and systems into each other. Albeit fundamental, the problem of finding the proper digital description of analog information is crucial to digital twinning. The latter is an emerging concept in the field of digital data processing that is regularly mentioned as key approach in the optimization of future communication technologies like 6G. We prove that 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 introduce a new digital description of analog signals and systems and prove it to be algorithmically more powerful than the traditional description based on Shannon's sampling approach.