How to plot the magnitude and phase of a given transfer function(z-domain)?

I tried approacting this by doing the LTI function:

>> z=tf('z'); >> H=0.203*[(1-z^-1)*(1-0.2743*z^-1+z^-2)]/[(1+0.2695*z^-1)*(1+0.4109*z^-1+0.6758*z^-2)]

H =

0.203 z^8 - 0.2587 z^7 + 0.2587 z^6 - 0.203 z^5
-----------------------------------------------
  z^8 + 0.6804 z^7 + 0.7865 z^6 + 0.1821 z^5

I don't even know if I'm approacting this right, please I need help in doing this.

[Daniel Ramirez]

I think I did it?

L=1000;
dw=2*pi/L;
w = -pi:dw:pi-dw;
aa=[1,0.6804,0.953486,0.182128];
bb=[0.2031,-0.2588,0.2588,-0.2031];
HH=freqz(bb,aa,w);
mag=abs(HH);title('Magnitude response')
figure
phase=angle(HH);title('Phase response')
plot(w,mag)
plot(w,phase)

The next step that they want me to do is plot the impulse response. So anyone know how to go from the freq domain to the time domain(n)? This is what I'm struggling the most, any help would be appreciated.

Answer 1

[Aik-Siong Koh]

The following links show how to get frequency domain plots from a transfer function.

https://www.mathworks.com/help/signal/ug/frequency-response.html

https://www.mathworks.com/help/ident/ref/lti.bode.html

The following links show how to get impulse response from transfer function.

https://www.mathworks.com/matlabcentral/answers/431809-how-to-simulate-an-impusles-response-of-a-transfer-function

https://www.mathworks.com/matlabcentral/answers/263498-impulse-response-from-transfer-function-in-matlab

The following links show how to get time domain from frequency domain.

https://www.mathworks.com/help/ident/ug/transforming-between-time-and-frequency-domain.html

https://www.mathworks.com/help/signal/ug/practical-introduction-to-frequency-domain-analysis.html

Additional comments from Siddharth Jawahar at MathWorks on 6/18/2024

You will need to define your transfer function using the ‘tf’ function which is also suitable for discrete-time systems by setting the ‘z’ variable and specifying the sample time. Then for the magnitude and the phase plots you can use the ‘bode’ plot command.

See the MATLAB code example below:

% Numerator and Denominator coefficients
b = 0.2031 * conv([1, -1], [1, -0.2743, 1]);  % Convolution of numerator parts
a = conv([1, 0.2695], [1, 0.4109, 0.6758]);   % Convolution of denominator parts

% Sample time - Adjust based on your specific requirements
Ts = 1;

% Create a discrete-time transfer function model
H = tf(b, a, Ts, 'Variable', 'z^-1');

% Plot the Bode plot
figure;
bode(H);
title('Bode Plot of H(z)');
grid on;

Answer 2

[ANNALURU R R SREENIVASA MURTHY]

You can use 'imp' function to plot impulse response.