The Fourier transform of finite support signals, which are absolutely integrable or finite energy, can be obtained

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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 {Xi(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.

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