模拟信号与系统对数字孪生表示的要求
On the Need of Analog Signals and Systems for Digital-Twin Representations
摘要：
我们认为，不同的数字描述的模拟带限信号和系统相互转换的任务，严格应用数学可计算性理论。尽管非常基本，但问题出现在数字孪生的范围内，这是模拟信息数字处理领域的一个新兴概念，经常被提及为下一代网络物理系统及其应用领域的关键推动因素之一。在这种情况下，我们证明，基本数量，如峰均功率比和有界输入/有界输出范数，这决定了现实世界的模拟系统的行为，一般不能确定从系统的数字孪生，这取决于上述描述的选择。作为一个主要的结果，我们的特点的算法强度香农的采样类型表示为数字孪生实现，并介绍了一个新的数字孪生实现模拟信号和系统。我们发现存在两个数字的描述，这两个唯一的特点是一定的模拟系统，这样一个描述可以转换成其他算法，但反之亦然。
英文摘要：
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 appears 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.
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