Implementing factored form in MATLAB?

I have a z transform in rational form as shown in attached photo

and i want to convert it into factored form

How can i implement it in MATLAB? I learnt from a google resource that we should use "zp2sos"command but i am not satisfied because output of "zp2sos"command does not looks like factored form

[Walter Roberson]

By the way, you do not need to create an zpk intermediate form

z = tf('z');
H = (4*z^2+3*z+9)/(4*z^2+3*z-4)

H =
 
  4 z^2 + 3 z + 9
  ---------------
  4 z^2 + 3 z - 4
 
Sample time: unspecified
Discrete-time transfer function.

H = [H, z/H]       %just to give a more complicated system

H =
 
  From input 1 to output:
  4 z^2 + 3 z + 9
  ---------------
  4 z^2 + 3 z - 4
 
  From input 2 to output:
  4 z^3 + 3 z^2 - 4 z
  -------------------
    4 z^2 + 3 z + 9
 
Sample time: unspecified
Discrete-time transfer function.

HN = H.Numerator;
HD = H.Denominator;
HN = cellfun(@(C) C(find(C,1):end), HN, 'uniform', 0);  %trim leading 0
HD = cellfun(@(C) C(find(C,1):end), HD, 'uniform', 0);  %trim leading 0
Hsos = cellfun(@tf2sos, HN, HD, 'uniform', 0).';
celldisp(Hsos)

 
Hsos{1} =
 
    1.0000    0.7500    2.2500    1.0000    0.7500   -1.0000

 
 
Hsos{2} =
 
    1.0000    0.7500   -1.0000    1.0000    0.7500    2.2500

 

Answer 1

[Abhishek]

Hi ABTJ,

From my understanding of the question, you want to convert the unfactored Z-transform representation into its factored form. Here is how it can be achieved using MATLAB’s Symbolic Math Toolbox:

b = [4 3 9]; % Numerator coefficient
a = [4 3 -4]; % Denominator coefficient 

[zeros,poles,gain] = tf2zp(b,a) % Convert the TF to pole-zero-gain form

zeros = 
  -0.3750 + 1.4524i
  -0.3750 - 1.4524i

poles = 2×1

-1.4430 0.6930

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gain = 1

syms z % Symbolic variable z
num = gain * prod(z - zeros) % Numerator of factored form 

num = 

den = prod(z - poles) % Denominator of factored form

den = 

factoredForm = num/den % TF in factored form

factoredForm = 

For more information on the Symbolic Math Toolbox and its capabilities, please refer to the MATLAB documentation:

https://www.mathworks.com/help/releases/r2024b/symbolic/index.html