Question

08 x 1.4 12 This is a two-dimensional plot of the z-plane that shows the unit circle, the real and imaginary axes, and the position of the system's poles and zeros. Zeros are typically marked with an 'o,, while poles are indicated with an X'. Sometimes, a location has multiple poles and zeros. In this case, a number is marked next to that location to indicate how many poles or zeros exist there. The above figure, for instance, shows four zeros (two conjugate pairs), one"trivial" pole at the origin, and one other conjugate pair of poles. Question: Where in the complex plane can zeros and poles be placed to have the strongest influence on the magnitude response of the filter?

Answer 1

The magnitude of filter response is high if the poles are at frequencies near the angles of poles, if the poles are near the unit circle.

The magnitude of filter response is low if zeros are placed near the unit circle.

The poles in the plane will push up the surface and zeros will pull down the surface.

So if we need magnitude response to high, then tgret should be poles where ever we need the response to be high.

Kindly upvote if it's helpful for you.