Phase Matching

The questions below are due on Thursday March 20, 2025; 02:00:00 PM.
 
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Below, we plot the angles of the DTFT of some signal x[\cdot]. The following plot shows \angle X(\Omega) as a function of \Omega, for -\pi < \Omega < \pi:

For each of the following signals, indicate which of the plots below, if any, is the plot of the angles of that signal's DTFT. If none of the graphs matches, select none instead. If there is not enough information to determine the answer, choose NEI (for "Not Enough Information") instead.

x_1[n] = -x[n]
Matching Graph:

x_2[n] = jx[n]
Matching Graph:

x_3[n] = 2x[n]
Matching Graph:

x_4[n] = x[n - 2]
Matching Graph:

x_5[n] = 2 + x[n]
Matching Graph:

x_6[n] = \begin{cases} x[n/3] & \text{if}~n \mod 3 = 0\\ 0 & \text{otherwise}\end{cases}
Matching Graph:

 

Graphs for Matching: