Fourier Match

The magnitude and angle of the Fourier transform of a signal x(t) are given in the following plots.

Five signals are derived from x(t):

\quad\quad\displaystyle x_1(t) = {dx(t)\over dt}

\quad\quad\displaystyle x_2(t) = (x*x)(t)

\quad\quad\displaystyle x_3(t) = x\left(t-{\pi\over2}\right)

\quad\quad\displaystyle x_4(t) = x(2t)

\quad\quad\displaystyle x_5(t) = x^2(t)

Seven magnitude plots (M1-M7) and seven angle plots (A1-A7) are shown below. Determine which of these plots is associated with each of the derived signals.

Part a. Which plot shows the magnitude of the Fourier transform of dx(t)\over dt?

Part b. Which plot shows the angle of the Fourier transform of dx(t)\over dt?

Part c. Which plot shows the magnitude of the Fourier transform of (x*x)(t)?

Part d. Which plot shows the angle of the Fourier transform of (x*x)(t)?

Part e. Which plot shows the magnitude of the Fourier transform of x\left(t-{\pi\over2}\right)?

Part f. Which plot shows the angle of the Fourier transform of x\left(t-{\pi\over2}\right)?

Part g. Which plot shows the magnitude of the Fourier transform of x(2t)?

Part h. Which plot shows the angle of the Fourier transform of x(2t)?

Part i. Which plot shows the magnitude of the Fourier transform of x^2(t)?

Part j. Which plot shows the angle of the Fourier transform of x^2(t)?

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