Question: The derivative property can be used to simplify the computation of some Fourier transforms. Let x(t) = r(t) 2r(t 1) + r(t

The derivative property can be used to simplify the computation of some Fourier transforms. Let

x(t) = r(t) − 2r(t − 1) + r(t − 2)

(a) Find and plot the second derivative with respect to tof x(t), y(t) = d2x(t)/dt2.

(b) Find X(Ω) from Y(Ω)using the derivative property.

(c) Verify the above result by computing the Fourier transform X(Ω) directly from x(t) using the Laplace transform.

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