Dielectric spectroscopy data treatment: I. Frequency domain

The computational methods for complex dielectric permittivity data treatment are considered in this paper. The dielectric spectroscopy data analysis in the frequency domain can be reduced to the problem of choosing the appropriate model functions and an estimation of their model parameters. To address the latter problem a method has been formulated based on a penalized maximum likelihood approach, for obtaining a smooth estimate for the model parameters expressed as functions of temperature. The use of the Hilbert transform (Kramers-Kronig relation) for dc conductivity evaluation directly from the complex dielectric permittivity data has been explored as well. In this paper a numerical algorithm for this procedure, using the fast Fourier transforms and a suitable interpolation technique, is suggested. Based on these methods, state-of-the-art software for dielectric spectroscopy data analysis in the frequency domain has been developed.