How I can plot the magnitude and phase response of the transfer function

can someone help me figure this out.

Answer 1

[Star Strider]

Try this:

z = tf('z',-1);
H = tf((0.0534*(1+z^-1)*(1-10166*z^-1 + z^-2))/((1-0.683*z^-1)*(1-1.4461*z^-1+0.7957*z^-2)))
H.Variable = 'z^-1'

bode(H)

[Mohsen Salimy]

Thank you for your help.

I have tried it but got an error see below.

Perhaps z is not defined. since my started my intialising the transfer function domain of the IIR filter - below:

%numerator coefficients

b0 = 0.05634;

b1 = [1 1];

b2 = [1 -1.0166 1];

%denominator coefficients

a1 = [1 -0.683];

a2 = [1 -1.4461 0.7957];

[Mohsen Salimy]

As previosuly i hadnt had Control system Toolbox.Just installed and it worked.

Although I am not so sure if we are answering the questions propely. I will attach the whole question here again, as this question is manily focused on Digtal signal Processing etc..

[Star Strider]

I assumed that you have the Control System Toolbox, and you want to use it to produce a Bode plot of your transfer function.

To create a Bode plot from the numerator and denominator coefficients:

z = tf('z',-1);
H = tf((0.0534*(1+z^-1)*(1-10166*z^-1 + z^-2))/((1-0.683*z^-1)*(1-1.4461*z^-1+0.7957*z^-2)))
H.Variable = 'z^-1'
num_zinv = H.Numerator{:}
den_zinv = H.Denominator{:}

figure
freqz(num_zinv, den_zinv, 2^14)                         % Filter Transfer Function: ‘z^-1’ Convention

%numerator coefficients 
b0 = 0.05634;
b1 = [1  1];
b2 = [1 -1.0166 1];
 %denominator coefficients
a1 = [1 -0.683];
a2 = [1 -1.4461 0.7957];

num = b0 * conv(b1,b2);
den = conv(a1,a2);

figure
freqz(num, den, 2^14)

Using the ‘z^-1’ representation (provided by the Control System Toolbox conversion):

num_zinv = 1.0e+02 * [0.000534000000000  -5.428110000000000  -5.428110000000000   0.000534000000000];

den_zinv = [1.000000000000000  -2.129100000000000   1.783386300000000  -0.543463100000000];

See the documentation on the freqz function to understand how to get outputs from it. The Signal Processing Toolbox does not (to my knowledge) have the ability to use ‘z^-1’ representation, so I used those provided by the Control System Toolbox.

[Mohsen Salimy]

Thank you so much I think this looks much like it...

[Star Strider]

As always, my pleasure!