Time Domain Version of the Bertoni´s Frequency Domain Hill Model

In the paper we present the way of obtaining the time domain model of the Bertoni´s frequency domain model of the hill presented in (H.L. Bertoni, 2000). Direct time domain analyses are more convenient when we consider the UWB propagation mechanism. The Bertoni´s frequency domain model was derived through the usage of the uniform theory of diffraction (UTD) presented by P. H. Pathak (1979). Here the model is used as an example of a smooth convex obstacle. The impulse response of the Bertoni´s hill model is determined in the paper in a closed analytical form. It is done through a transformation of the frequency domain model by means of one-sided inverse Fourier transform (P.H. Pathak, 1995). Then the correctness of the derived impulse response of the hill is verified by comparison of it with the inverse fast Fourier transform (IFFT) of the frequency response of the considered channel model.