# DFT problem help

I had this problem on a previous midterm but I can't seem to get the correct answer. The answers are shown in red provided by the professor. I've attempted it two different ways: one by having my limit from from 0 to (17-1) then tried by setting limit to 0 to (13-1) by truncating values before zero. I don't believe I'm approaching this problem correctly and need some guidance.

Thank you

• What does $X[k=10]$ mean? I can't say I have ever seen that notation before. Dec 18, 2017 at 1:57
• It's just X[10] or X(10). Capital X representing the DFT result of lower case x. i1.wp.com/audiograins.com/blog/wp-content/uploads/2014/01/… Dec 18, 2017 at 2:03

In my opinion, the problem is not clearly specified because it remains a bit unclear which DFT length $N$ you're supposed to use. From the figure and from the given solution one can guess that $N=16$. So the time domain vector is
x = [0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3]
X = [24,0,0,0,-8+8i,0,0,0,-8,0,0,0,-8-8i,0,0,0]
corresponding to the given solution. Since you're asked to specify magnitude and phase, you should compute the magnitude and phase of $X[12]=-8-8i$.