Problem 3.18: Use the convolution property to find the FT of the system output, either Y(jω) or Y(e^{jΩ}), for the following inputs and system impulse responses:
(a) x(t) = 3e^{-t}u(t) and h(t) = 2e^{-2t}u(t).
(b) x[n] = (1/2)^n u[n] and h[n] = (1/(πn))sin(πn/2).
Answers:
(a) Y(jω) = (2 / (jω + 2))(3 / (jω + 1))
(b) Y(e^{jΩ}) = { 1/(1 - (1/2)e^{-jΩ}), |Ω| ≤ π/2; 0, π/2 < |Ω| ≤ π