Give the fourier transform of the signals that can be obtain

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Reference no: EM13278974

Any causal signal x(t) having a Laplace transform with poles in the open-left s-plane (i.e., not including the jΩ axis) has, as we saw before, a region of convergence that includes the jΩ axis, and as such its Fourier transform can be found from its Laplace transform. Consider the following signals:
x1(t) = e-2tu(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) indicating 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.

Reference no: EM13278974

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