The Fourier transform of finite support signals, which are absolutely integrable or finite energy, can be obtained from their Laplace transform rather than doing the integral. Consider the following signals

x₁(t) = u(t + 0.5) − u(t − 0.5), x₂(t) = sin(2π t) [u(t) − u(t − 0.5)]

x₃(t) = r(t + 1) − 2r(t) + r(t − 1)

(a) Plot each of the above signals.

(b) Find the Fourier transforms {X_i(Ω)}for i = 1, 2, and 3 using the Laplace transform.

(c) Use MATLAB’s symbolic integration function int to compute the Fourier transform of the given signals. Plot the magnitude spectrum corresponding to each of the signals.