Considering Phase

The questions below are due on Thursday March 20, 2025; 02:00:00 PM.
 
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Part a. Determine x_1(t), whose Fourier transform X_1(\omega) has the following magnitude and angle.

Notice that the angle of X_1(\omega) is only defined for |\omega|\lt3\pi since the magnitude of X_1(\omega) is zero outside that range.

Express x_1(t) as a closed-form function of time.

Part b. Determine x_2(t), whose Fourier transform X_2(\omega) has the following magnitude and angle.

Express x_2(t) as a closed-form function of time.

Part c. What are important similarities and differences between x_1(t) and x_2(t)? How do those similarities and differences manifest in their Fourier transforms?

Please upload a single pdf file that contains your answers to all parts of this problem:

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