I desire to derive the values of the real permittivity from the imaginary permittivity ore vice versa using KK relations. It is known in KK equations that the integrands are defined in the bound [0,inf.] , but in practical applications, we do not have infinite frequencies and therefore the measured values will be different than the analytical values. So how can we apply the KK relations in a small frequency range [w1,w2], where w1>>0 and w2
You are only to calculate one additional unknown constant C from an experimental data. See attached file for some explanation
Thanks very much @Konstantin, in this case i can not calculate the real and imaginary parts of the permittivity analytically or numerically, and consequently i will need for measured date to find the rest of the integrand. Also why it is assumed in the attached file that the imaginary part is added to the real part? why not subtracted?
I know that the imaginary part refers to the losses therefore should be subtracted.
The sign of relation depends on definition. See for example the last phrases in http://www.iam.kit.edu/wet/plainhtml/Download/Derivation_Kramers-Kronig.pdf
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