# Transfer function to pole zero diagram

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Jonathan George on 26 Mar 2022
Answered: Paul on 26 Mar 2022
Is there any way to represent a discrete-domain transfer function [H(z)] with a pole zero diagram in MATLAB? And perhaps even vice-versa?

Paul on 26 Mar 2022
The answer to the first question is to use pzplot()
H = tf([1 .5],[1 2.5 3.125],1)
H = z + 0.5 ------------------- z^2 + 2.5 z + 3.125 Sample time: 1 seconds Discrete-time transfer function.
pzplot(H)
axis equal Not sure about the second question. How would the pole-zero diagram be represented in Matlab for input to some function from which the tf is computed? If the poles and zeros are known then
z = -0.5; p = -1.25 + 1j*[1.25 -1.25];
H = zpk(z,p,1,1)
H = (z+0.5) -------------------- (z^2 + 2.5z + 3.125) Sample time: 1 seconds Discrete-time zero/pole/gain model.
H = tf(H)
H = z + 0.5 ------------------- z^2 + 2.5 z + 3.125 Sample time: 1 seconds Discrete-time transfer function.

R2021b

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