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

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Cola on 13 Mar 2022
Commented: William Rose on 14 Mar 2022
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)

William Rose on 13 Mar 2022
You don't need to multiply the function by its complex conjugate to get a purely real denominator. Just divide complex numerator by the complex denominator, to get a new complex number, and take the abs() of it.
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Cola on 14 Mar 2022
Edited: Cola on 14 Mar 2022
@William Rose Thank you so much.
William Rose on 14 Mar 2022
@Cola, you're welcome, and good luck with your work.

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
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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().
Cola on 14 Mar 2022
Edited: Cola on 14 Mar 2022
@Paul @William Rose Thanks to you. And we also can use the order 'freqs' to calculate the norm.