# Laplace and Fourier transform of a Signal

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Any causal signal x(t) having a Laplace transform with poles in the open-left s-plane (i.e., not including the j? axis) has, as we saw before, a region of convergence that includes the j? axis, and as such its Fourier transform 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 (use properties of the Laplace transform) including the 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.

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This solution is related to the Laplace and Fourier transforms of signals.

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