A causal signal x(t) having a Laplace transform with poles in the open-left s-plane (i.e., not including the j-axis) has a Fourier transform that can

A causal signal x(t) having a Laplace transform with poles in the open-left s-plane (i.e., not including the j­Ω-axis) has a Fourier transform that can be found from its Laplace transform. Consider the following signals

x₁(t) = e^−2t u(t),              x₂(t) = r(t),          x₃(t) = x₁(t) x₂(t)

(a) Determine the Laplace transform of the above signals indicating their corresponding region of convergence.

(b) Determine for which of these signals you can find its Fourier transform from its Laplace transform. Explain.

(c) Give the Fourier transform of the signals that can be obtained from their Laplace transform.