-1
$\begingroup$

Just wanted to make sure:

This cases would have three poles at the exact same location of (z=1) on the complex plane?

$H(z)=\frac{1}{(z-1)^3}$

But this case, would have three poles spread out on a circle of complex plane:

$H(z)=\frac{1}{z^3-1}$

$H(z)=\frac{1}{\left(z-1\right)\left(z-0.5-i\sqrt3/2\right)\left(z-0.5+i\sqrt3/2\right)}$

$\endgroup$
1
$\begingroup$

Exactly. In the first case you have all 3 poles $z_{1,2,3}=1$ in a real part of the complex plane. enter image description here

In the second one you have the poles spread on the circle as you suggested

$z_1 = 1$ , $z_2 = - \frac{1}{2} + \frac{1}{2}\cdot\sqrt{3}i$, $z_3 = - \frac{1}{2} - \frac{1}{2}\cdot\sqrt{3}i$

enter image description here

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.