How to enter vector coefficients to z-transform

I have this z-tf:

Hz = g *(1 + 2*z^-1 + z^-2) / ( 1 + a1*z^-1 + a2*z^-2)

where g = [2,2.2,2.3] , a1 = [2, 5,8] and a2 =[ 1,0.3,0.4]

how can I get all 4's Hz (TF) directly by using the vector coeficients?

[Paul]

Hi TeraWatt,

Seems like there should only be three transfer functions.

What is the desired form? A single system with three inputs and three outputs? An 3-element array of single-input/single-outpu transfer functions? Something else?

[TeraWatt]

I would like to see the numerator and denomitaor as multiple of z^(-1).

The system will receive three inputs and should respond with three outputs , each one independent from the other two

Answer 1

[Walter Roberson]

z = tf('z')

z =
 
  z
 
Sample time: unspecified
Discrete-time transfer function.

g = [2,2.2,2.3] .';
a1 = [2, 5,8] .';
a2 =[ 1,0.3,0.4] .';
HZ = arrayfun(@(G,A1,A2) G * (1 + 2*z^-1 + z^-2) / ( 1 + A1*z^-1 + A2*z^-2), g, a1, a2, 'uniform', 0);
HZ = vertcat(HZ{:})

HZ =
 
  From input to output...
       2 z^6 + 4 z^5 + 2 z^4
   1:  ---------------------
         z^6 + 2 z^5 + z^4
 
       2.2 z^6 + 4.4 z^5 + 2.2 z^4
   2:  ---------------------------
          z^6 + 5 z^5 + 0.3 z^4
 
       2.3 z^6 + 4.6 z^5 + 2.3 z^4
   3:  ---------------------------
          z^6 + 8 z^5 + 0.4 z^4
 
Sample time: unspecified
Discrete-time transfer function.

[TeraWatt]

Thanks very much. it works.

One more thing, How to force the elements of the numerator and denominator as multiple of z^(-1)?

Answer 2

[Paul]

g = [2,2.2,2.3];
a1 = [2, 5,8];
a2 =[ 1,0.3,0.4];
HZ = tf(zeros(3),'Ts',-1);
for ii = 1:3
    HZ(ii,ii) = tf(g(ii)*[1 2 1],[1 a1(ii) a2(ii)],-1,'Variable','z^-1');
end
HZ

HZ =
 
  From input 1 to output...
       2 + 4 z^-1 + 2 z^-2
   1:  -------------------
        1 + 2 z^-1 + z^-2
 
   2:  0
 
   3:  0
 
  From input 2 to output...
   1:  0
 
       2.2 + 4.4 z^-1 + 2.2 z^-2
   2:  -------------------------
         1 + 5 z^-1 + 0.3 z^-2
 
   3:  0
 
  From input 3 to output...
   1:  0
 
   2:  0
 
       2.3 + 4.6 z^-1 + 2.3 z^-2
   3:  -------------------------
         1 + 8 z^-1 + 0.4 z^-2
 
Sample time: unspecified
Discrete-time transfer function.