Determination of the step response function of a dielectric in the presence of noise

In the time domain characterization of dielectrics a fundamental measure is the dielectric response function Φ(t). This function permits the relaxation time and the complex permittivity of the dielectric under test to be determined, allowing the complete characterization of the dielectric properties. To calculate the Φ(t) function a time domain deconvolution algorithm (TDD), developed in a previous work, is employed. In this paper a new technique to enhance the calculation of the Φ(t) function in the time domain, is presented, avoiding the instability problems inherent to the TDD algorithm. The method consists in the use of appropriate digital lowpass filter in several stages of the time domain deconvolution algorithm to calculate the Φ(t) function. This procedure provides an enhanced precision for Φ(t) even for very short times (≈ 10 ps for the time domain reflectometry system used).