Analytic impulsive time-domain UTD coefficient for pyramid-vertex diffraction

We introduce our solution for the diffraction of a pulsed ray field, with spherical wavefront, by the vertex (tip) of a pyramid. Within the Uniform Geometrical Theory of Diffraction (UTD) we improve the time domain (TD) solutions available in the literature by introducing the field diffracted by a perfectly conducting faceted structure made by interconnected flat plates, for source and observation points at finite distance from the tip. The proposed closed form expression for an exciting impulsive source has been calculated by employing the one-sided inverse Fourier transform of the frequency domain solution. The solution obtained is able to compensate for the discontinuities of the field predicted by standard TD-UTD, i.e., time domain geometrical optics (TD-GO) combined with the TD-UTD wedge singly diffracted rays.