# How to calculate the norm of the transfer function in frequency domain?

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To calculate the norm of the transfer function by substituting s=jω is troublesome, especially for some complicated transfer functions. Is there a way to calculate the norm directly? Thanks!

For example, transfer funciton:

Substituting s=jω，

then,

Thus we can plot the figure in frequency domain,

Matlab code:

omega=0:0.01:10;

G1_N=0.25e-2 .* omega .^ 2 + 0.1e1;

G1_D=((2 .* omega) - 0.15e0 .* (omega .^ 3)) .^ 2 + (0.1e1 + 0.5e-2 .* (omega .^ 4) - (omega .^ 2)) .^ 2;

G1=sqrt(G1_N ./ G1_D);

plot(omega,G1)

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### Accepted Answer

William Rose
on 13 Mar 2022

##### 3 Comments

### More Answers (1)

Paul
on 13 Mar 2022

Check out

doc tf

to learn how to create a transfer function (tf) object. Once you have G(s) defined as a tf object use bode() to compute its magnitude (and phase if desired)

doc bode

##### 3 Comments

Paul
on 13 Mar 2022

Actually, I was thinking of the Control System Toolbox. I'm not famiiar with the System ID toolbox.

If just wanting to use base Matlab, I'd probably use polyval().

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