How can I draw the transfer function spectra by matlab?

[Paul]

Hi Anna,

Do you know how to create a tf object in Matlab?

Do you have a definition of "spectra" as used in this context?

[Sam Chak]

Guess that is the plural of 'spectrum' borrowed from the world of physics and electronics, and it has something to with the frequency response of the digital filter (because it is shown in the z-domain).

[Paul]

Yes, the fact that "spectra" is plural adds uncertainty into the question. Do you think spectra/spectrum has "something to [do] with the frequency response" or do you think it is the frequency response? FWIW, I'm more inclined to refer to the spectrum of a signal, not a a system (unless the spectrum of a system is just the spectrum of its impulse response?).

[Sam Chak]

I remember that when we want to analyze the frequency content of a signal, the term "signal spectrum" is often used, and we usually plot the signal amplitude vs. its corresponding frequency. Almost similar to what is shown here:

https://www.mathworks.com/help/matlab/math/basic-spectral-analysis.html

Perhaps the question asks to show the spectrum of the signal coming out from the digital filter. Let @Anna to clarify.

Answer 1

[Star Strider]

The ‘spectrum’ is the Bode plot:

z = tf('z');
H = 5 / (1 + 2*cos(5)*z^-1 + z^-2);
H.Variable = 'z^-1'

H =
 
            5
  ----------------------
  1 + 0.5673 z^-1 + z^-2
 
Sample time: unspecified
Discrete-time transfer function.

figure
bodeplot(H)
grid

See the documentation on bode and bodeplot for details.

.

[Anna]

can you explain for me the line H.Variable = 'z^-1'

thank you!!

[Star Strider]

That selects how the variable is formatted. See the documentation section on Variable for a full explanation.

Also, I am assuming here that you are implementing a discrete control system. If instead you are coding a digital filter. the freqz function is most appropriate —

b = [5 0 0 0];
a = [1 2*cos(5) 1 0];

figure
freqz(b, a, 2^16)

% set(subplot(2,1,1), 'XScale','log')                     % Optional
% set(subplot(2,1,2), 'XScale','log')                     % Optional

.