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Ultra-wideband (UWB) has potential applications in a variety of medical areas such as implant wireless sensors, microwave hyperthermia, imaging and radar. The wave propagation inside the human body must be known for an efficient system design of these different e-health applications. Nevertheless, little is known about the propagation of UWB signals inside the human body despite the enormous research efforts devoted to characterising radio propagation around the body. Therefore in this study, the UWB wave propagation through the human chest is characterised by electromagnetic simulations. For this sake, a voxel model of the human body that incorporates the frequency-dependent material properties of the human tissues is used. The wave propagation for line-of-sight (LOS) scenarios in the frequency bands of 100-1000 MHz and 1-5 GHz are evaluated. Both vertical and horizontal wave polarisations are considered. The power radiographs of the received signals inside the human chest are presented, which display the frequency and polarisation-dependent variations. The spectral analysis of the received signals reveals that the frequency range of 100-250 MHz, offers the minimum propagation loss. This frequency range of 250-1000 MHz is depicted as a region with less variant loss against frequency. Furthermore, the power delay profile (PDP) and the root mean square delay spread of the in-body channels is presented for different depths inside the body. These insightful results further the understanding of the propagation behaviour of UWB signals inside the human body, which will ease the development of in-body e-health applications.