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True/False

The questions below are due on Monday March 29, 2021; 10:00:00 PM.
 
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Note that this exercise is intended to be solved by hand, without the use of computation.

Determine whether the following properties hold for each of the signals below.

Property 1: X(0)=0

Property 2: \int_{-\pi}^\pi X(\Omega)\,d\Omega=0

Property 3: X(\Omega) is purely imaginary

Property 4: e^{\,jk\Omega}X(\Omega) is purely real for some integer k

Indicate which of the four properties hold for x_1:
1
2
3
4

Indicate which of the four properties hold for x_2:
1
2
3
4

Indicate which of the four properties hold for x_3:
1
2
3
4

Indicate which of the four properties hold for x_4:
1
2
3
4