Find the LT and specify ROC of:(adsbygoogle = window.adsbygoogle || []).push({});

x(t) = e^{-at}, 0 ≤ t ≤ T

= 0, elsewhere

where a > 0

Attempt:

X(s) = - 1/(s+a)*e^{-(s+a)}integrated from 0 to T

=> -1/(s+a)[e^{-(s+a)}+ 1]

Converges to X(s) = 1/(s+a) , a ⊂ R, if Re{s} > -a for 0≤t≤T

Elsewhere ROC is empty (LT doesn't exist).

Is this correct?

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# Laplace transform and region of convergence

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