Implementing factored form in MATLAB?

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ABTJ 2021-3-10

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https://ww2.mathworks.cn/matlabcentral/answers/768097-implementing-factored-form-in-matlab

评论： Walter Roberson 2021-3-10

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

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Walter Roberson 2021-3-10

在 MATLAB Online 中打开

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

 