Interpretation and separability of the effective permittivity in case that both permittivity and conductivity are complex

The paper is about the interpretation and separability of the effective permittivity in case that both the permittivity and the conductivity are dispersive and thus complex-valued. It is shown that: a) it is always possible to retrieve the static conductivity and the high-frequency (optical) permittivity from the effective permittivity; b) it is in general not possible to separate the complex conductivity from the complex permittivity. The findings rely on the application of the Hilbert transform and their effectiveness is verified by means of a numerical example.