Problem 3 a) Find the poles and zeros of the following Laplace-transforms: X(s) = s+3 (s-2)(s+3) s²+2s+1 Y(s) = (s + 2)²+1 2 3 Z(s) + s+1 S-2 b) Find the inverse Laplace-transform of the following: X(s) = 2e-2s (s+1)²+2 s²+1 (s+1)3 c) The transfer function of an LTI system is: + S H(s) = (s + 1)²+1 i) Find the unit-step response. ii) Find the response to the following inputs x(t) = u(t) - u(t - 2) x2(t) = d(t)+d(t-3) x3(t) = 2r(t)