Create a transfer function that looks like a polynomial

Hello everyone I have a function called C

C=inv(Psi'*Psi)*Psi'*E1;

The challege I am having is creating a transfer function from C called filterC that looks like the picture that is attached.

Note the picture attached is an example. My values will be different.

whenever I do prefilter=tf(C) I get values like in row form

Prefilter=tf(C)

Prefilter =
 
  From input to output...
   1:  -0.8673
 
   2:  0.3917
 
   3:  0.2832
 
   4:  -0.6459
 
   5:  -0.08966
 
Static gain.

How can I get my transfer function to look similar to this?

Am I doing something wrong?

Any help is greatly appreciated.

Answer 1

[Ameer Hamza]

If you have filter cofficient, then you need to pass following options to tf()

C = [1 -1.047 0.558 0.2608 -0.7408 0.09526];
sys = tf(C, 1, .01, 'variable', 'z^-1')

Result

>> sys

sys =
 
  1 - 1.047 z^-1 + 0.558 z^-2 + 0.2608 z^-3 - 0.7408 z^-4 + 0.09526 z^-5
 
Sample time: 0.01 seconds
Discrete-time transfer function.

Note that, in this case, C must be a row vector.

In your question, you are using C as a column vector; therefore, you are getting five transfer functions with static gains.

[Heraldo Tello]

I believe you are on the right track. I converted the column vector into a row vector.

C'

ans =

   -0.8673    0.3917    0.2832   -0.6459   -0.0897

However when I do the transfer function, I only get up to z^-4 which is the wrong order. I know I should get up to z^-5 (five back samples) with the first one being one.

filterC=tf(C', 1, .01, 'variable', 'z^-1')

filterC =
 
  -0.8673 + 0.3917 z^-1 + 0.2832 z^-2 - 0.6459 z^-3 - 0.08966 z^-4

I believe it should look like like

[Heraldo Tello]

I believe it should look like this

filterC = 1 - 0.8673 z^-1 + 0.3917 z^-2 + 0.2832 z^-3 + 0.6459 z^-4 + 0.08966 z^-5

[Ameer Hamza]

You can make it like this by adding a 1 at the beginning of cofficients vector

filterC=tf([1 C'], 1, .01, 'variable', 'z^-1')

Answer 2

[Star Strider]

Since it is a ‘static gain’ object, it acts just like a simple amplifier. It has no frequency-dependent characteristics, so it has no variable associated with it.