getting z transform in factored form?using Matlab?

How we can get z transform in factored form if we have z,p and k?I have also attached snapshot of z transform below

I can use matlab command tf2zp for finding z,p and k.

(z,p,k)=tf2zp(n,d) where n=numerator of H(z) and d=denominator of H(z)

But from there onwards how can i then proceed to find factored form?

Is it better to use matlab function zp2sos ??

[Walter Roberson]

poly2sym() and factor()?

Answer 1

[Star Strider]

Control System Toolbox:

z = tf('z');
H = (4*z^2 + 3*z + 9) / (4*z^2 + 3*z - 4);
zsys = zpk(H);
Z = [zsys.Z{:}]
P = [zsys.P{:}]
K = zsys.K


Z =
                     -0.375 +      1.45236875482778i
                     -0.375 -      1.45236875482778i

P =
         -1.44300046816469
         0.693000468164691

K =
     1

[ABTJ]

I get error when i copy paste your code

[Star Strider]

My code obviously works in R2019b.

Try this instead:

Z = cell2mat(zsys.Z)
P = cell2mat(zsys.P)
K = zsys.K

Answer 2

[Abhishek]

Hi ABTJ,

I understand that you want to express the Z-transform in factored form after determining the zero, poles and gain using the “tf2zp” function. The following MATLAB Answer explains how to do the same:

https://www.mathworks.com/matlabcentral/answers/768097-implementing-factored-form-in-matlab?s_tid=srchtitle