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Unit step signal or function u(t) appears in many fields, which plays an important role in the research and solution of many problems. But for a long time, this signal has a clear definition when t ≠ 0, but there is no definite definition at t=0 - this paper calls it u (0) uncertainty. Although u (0) uncertainty will not affect the application and related theoretical research of u (t) in many cases, we find that it will do in some cases. We also find that the definite definition of u (0) has been implied in the existing basic theory of signals and systems, that is, u (0) =1/2. A physical meaning of u(0) =1/2 is also given by the double switch circuit. This paper makes the understanding of u(t) and its related theory more profound, comprehensive and accurate, and lays a more solid foundation for establishing a more perfect theoretical system of information, signal, system and so on.
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