# 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.
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
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.