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I am currently studying for an exam for a Speech Processing course I am taking and stumbled across this question in one of the sample exams:

Question

I began to plot the pole-zero configuration placing my poles on the unit circle at points +j and -j as well as placing my zero in the 0.5 location.

When I compared my plot to his, I noticed that he placed the poles instead in the halfway point of the Imaginary axis and was wondering why he decided to place them there?

Here is my professors answer:

Answer

Thanks

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    $\begingroup$ your prof was wrong. $\endgroup$ – robert bristow-johnson Feb 23 '17 at 1:11
  • $\begingroup$ Poles on the unit circle means that the filter is unstable. Maybe your prof was allergic to this :-) $\endgroup$ – Hilmar Feb 23 '17 at 13:12
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If the dotted-line circle is the unity circle and both the real and imaginary axis are on the same scale, then your professor's answer is wrong.

Your solution is the correct one. It would be something like this:

enter image description here

where the dotted-line circle has a radius $r=1$.

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  • $\begingroup$ Thanks for the clarification. Thought I was going crazy for a second $\endgroup$ – User 5842 Feb 23 '17 at 1:12

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