Turing computability deals with the question of what is theoretically computable on a digital computer, and hence is relevant whenever digital hardware is used. In this paper we study different possibilities to define computable bandlimited signals and systems. We consider a definition that uses finite Shannon sampling series as approximating functions and another that employs computable continuous functions together with an effectively computable time concentration. We discuss the advantages and drawbacks of both definitions and analyze the connections and differences. In particular, we show that both definitions are equivalent for many practically relevant signal classes, e.g. for bandlimited signals with finite energy, but also that there are important differences, such as for the impulse responses of BIBO stable LTI systems.

中文翻译：

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带限信号和系统的可计算时间浓度

图灵可计算性处理的是什么在数字计算机上理论上可计算的问题，因此无论何时使用数字硬件都是相关的。在本文中，我们研究了定义可计算带限信号和系统的不同可能性。我们考虑使用有限香农采样序列作为近似函数的定义，以及使用可计算的连续函数和有效可计算的时间集中度的另一个定义。我们讨论了这两种定义的优缺点，并分析了它们之间的联系和差异。特别是，我们表明这两个定义对于许多实际相关的信号类别是等效的，例如对于具有有限能量的带限信号，但也存在重要差异，例如对于 BIBO 稳定 LTI 系统的脉冲响应。