Analyzing the effect of Hilbert transform on diffraction of a plane wave by an oscillating half-plane

In this study, we are analyzing the effect of the Hilbert Transform (HT) on diffraction of a plane wave by an oscillating half-plane. Both the incident wave and oscillating half-plane have different oscillating frequencies. After the necessary mathematical computations for several types of time-dependent oscillating functions, it is verified graphically that the HT induces a shift of [Formula: see text], which can be observed from the flipping effect in the magnitude of the sinusoidal components occurring in their respective diffracted fields. Graphical illustrations presenting the effects of the HT are presented and discussed.