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Laplace transform of a pulse

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Consider computing the Laplace transform of a pulse:

p(t) = {1 0 < t < 1
{0 otherwise

a) use the integral formula to find P(s), the Laplace transform of p(t). Determine the region of convergence of P(s).
b)Represent p(t) in terms of the unit-step function and use its Laplace transform and the time-shift property to find P(s). Find the poles and zeros of P(s) to verify the region of convergence obtained above.

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