Step Response from the Impulse Response

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SUMMARY

The discussion focuses on deriving the step response from the impulse response using Laplace transforms. The impulse response function given is h(t) = e^{-a |t|}, which raises concerns about causality since it is non-zero for t < 0. The correct approach involves recognizing that the time derivative of the step response corresponds to the impulse response, leading to the conclusion that the integral of the impulse response yields the step response. The book answer provided is option A, which the user finds confusing due to the presence of the term e^{at}.

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Homework Statement


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Homework Equations


Use Laplace then multiply in laplace domain then do laplace inverse

The Attempt at a Solution


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Book answer is A
I don't get the first term of eat in option A.[/B]
 

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The way I know how to do this is the time derivative of the step response is the impulse response, so that the integral of the impulse response is the step response. I am a little puzzled by the ## h(t)= e^{-a |t|} ## impulse response function. Normally, I think the impulse response should be zero for ## t<0 ## , or it violates causality.
 

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