Laplace transform of a pulse
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.