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I have a 8th order s-domain transfer function that i would like to normalize for plotting a bode plot. The transfer function is in expanded form i.e. s^8 +s^7+s^6 etc.

i want to normalise the frequency f by frequency f0 such that s = j(f/f0) instead of just s = j2πf. the reason i want to do this is because i see some strange behaviour (asymptotes) if i plot the non-normalised version, so I am hoping this will solve the problem.

the thing I am unsure of is that, since my highest degree is 8 (in the denominator), is it as simple as dividing all the terms by (1/ω0)^8? is there some other methods that i can use since the transfer function is not one that is really simple to work with. (coefficients in the range of 1e-30)

OR

would i be extracting the 1/w0 factor out of my coefficients? i.e. if the term is 5s^2, would the normalised version be 5/(w0^2) s^2? (this compared to the above where i would have 5/(w0^8)s^2.

i suppose I am also curious if we normalise the plot, does j(w/w0) still equal to s? why does this still work?

thanks all