The discussion focuses on the application of the Laplace transform to anti-causal systems, specifically the function exp(t)u(-t). The unilateral Laplace transform integrates from 0 to infinity, which raises questions about the validity of applying it to functions defined for negative time. The key takeaway is that the Laplace transform can be applied to functions as long as the integral is defined, finite, and well-formed. The unit step function u(-t) is identified as the flipped unit step function, defined as u(-t) = 1 for -∞ < t ≤ 0.
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It is the flipped unit step function...u(-t)=1 -inf<t<=0DEvens said:What is the function u(-t) in your question?
The Laplace transform applies to functions. The variable is not a time variable, but simply an integration variable. It does not know what is the nature of those functions. If the integral is defined, finite, and well formed, then that's the transform. If it is not well formed or diverges or is not defined, then the same applies to the transform.
Depending on your application the Laplace transform may work just fine, may not be helpful, or may not be appropriate at all. It is very hard to tell from the small hints you have given.