A Kramers-Kronig integral relation turned into a simple convolution operation and its application to dielectric measurements

Abstract

This paper proposes that the conduction-free imaginary-part of dielectric constant may be obtained from a convolution between its real-part on a logarithmic scale of frequency and the hyperbolic cosecant function. This equation is, in fact, one of the Kramers-Kronig relations and is deduced from the relationships that relate a distribution of relaxation frequencies both to the real-part and to the conduction-free imaginary-part of the dielectric constant. This simple result has a large practical interest as it allows, for instance, checking for the presence of conductivity on experimental data.