Advanced algorithm development for transformation from the frequency domain into the time domain

Abstract

The thesis deals with the problem of calculating the potential distribution at a certain distance from a point impulse charge as well as from a point source of impulse current, which are described using the Heidler approximation. When transitioning from the time to the frequency domain, there is no analytical solution to the Heidler approximation, so the function is approximated on the basis of the natural logarithm e, where the application of the collocation method at the point combined with the least squares method yields unknown values ​​of the weight functions for the slope factors n <3, 4, …, 15> . The second chapter describes the impulse point charge in the time and frequency domains using the Heidler approximation, the transition from the frequency to the time domain using the inverse Fourier transform, and the analytical and numerical expression for the potential distribution at a selected distance from the impulse point charge, in the time domain. The tables show the values ​​of the approximation coefficients a1k and β1k and the values ​​of the approximation coefficients a2k and β2k for different steepness factors n <3, 4, …, 15> . Examples are made for calculating the accuracy of numerical integration, which translates the potential function from the frequency to the time domain. In the third chapter, a point source of pulsed current is described using the Heidler approximation of the lightning current, and a numerical expression for the potential distribution at a selected distance from the pulsed point source of current, in the time domain. Examples are made in which the potential in the time domain is numerically calculated for the same pulsed current, for a selected distance of the observed point from the pulsed current source.

Type