My question is similar to this one and this one, but neither answers address my concern.

Suppose you have a signal x(n) = {-1,2,-3,2,-1} where we can assume x(0) = -3. So this is an even signal.

How do you find the phase of the DFT of x(n)?

  • $\begingroup$ What you show is not an even signal, did you mean x(n) = {1,2,-3,2,1}? $\endgroup$ Mar 21, 2020 at 3:28
  • $\begingroup$ This post should help you: dsp.stackexchange.com/questions/38544/… $\endgroup$ Mar 21, 2020 at 3:29
  • $\begingroup$ Sorry my mistake. Now it's even $\endgroup$ Mar 21, 2020 at 3:30
  • $\begingroup$ @DanBoschen - I am not sure I see which part of the post is relevant to this question. So the answer to this question is $\pi$, but I'm not sure I see why. $\endgroup$ Mar 21, 2020 at 3:33
  • 1
    $\begingroup$ No problem, this was very helpful $\endgroup$ Mar 21, 2020 at 3:51

1 Answer 1


Here is a hint that will help you:

The DFT is cyclical in time and in frequency. For the sequence given by

$$x(n) = [-1,2,-3,2,-1]$$

With x(0) = -3 would be solved using the standard DFT equation that starts at n=0 using

$$x(n) = [-3, 2, -1,-1, 2]$$

From that you can solve for the DFT and then determine easily for each result what it's phase is.


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