An efficient algorithm for numerical computation of the complex dielectric permittivity using Hilbert transform and FFT techniques through Kramers Kronig relation

A procedure is described to efficiently obtain the complex dielectric permittivity of materials with routing available in the current software applications. This procedure calculates one component of the dielectric permittivity from its other components by making use of the Hilbert transform properties of the Kramers-Kronig relations. The mathematical technique used by the Kramers-Kronig relations, which allows one component to be defined in terms of the other, is Hilbert transform since ε\´(ω) and ε"(ω) can be shown to be Hilbert transform pairs. The practical formation of this Hilbert transform pair is not an easy task in most instances. One cannot produce an analytical function in order to obtain its Hilbert transformation over a large frequency range. An efficient algorithm is developed to obtain the complex dielectric permittivity of materials over a large frequency range. This paper deals with an algorithm that has been verified for both theoretically generated data (Debye equation) and measured data for various high temperature dielectric materials.