# Drawing the modulus from a Transfer function

As you may guess from my other questions i am a student so pardon me any ignorance and guide me to the truth. Thanks

In this exercise from an exam i was given that transfer function with poles and zeros. I was asked to draw the modulus and the "UHD imagive below the Transfer function" image was my answer.

I know that when you encounter a zero, you "go down" and when you encounter a pole you "go up" in the graph. When you encounter both "aligned", you get a cero as they cancel each other.

The answer from the teacher was that the maximum, which is 1, is at pi/8 (and -pi/8), not at pi/4, because at pi/4 (and -pi/4) he draw the minimum.

Why is that? and what i did got wrong or missed in my understanding?

EDIT: Here i add another example from a recent exam. I would like if someone could do a brief/short explanation in how to properly draw it and what should i know or notice.

The question is the same, but i lack proper understanding of it.

• You might find this answer useful in developing your understanding about the way poles and zeroes work together in a frequency response. – A_A Jan 23 '18 at 16:38
• So, "my maximum" that i set at pi/4 couldn't be because the function will go into the infinity? – WhiteGlove Jan 23 '18 at 16:43

Your sketch is not bad at all. I don't know why your teacher drew a "minimum" (do you mean a zero?) at $$\pi/4$$, because there shouldn't be any. The zeros are clearly at $$\pm\pi/2$$ and at $$\pi$$, and the main peak should indeed be close to $$\pi/4$$. By the way, I'm missing a pole. There are $$4$$ zeros and only $$3$$ poles. The fourth one should probably be at the origin. Maybe your teacher didn't give this exercise as much thought as he should have ...