Improving the data rate has been a major challenge in mud pulse telemetry. One of the reasons for the confinement in lower data rate is due to the lack of knowledge of the mud communication channel. Furthermore, the mud property, drill string geometry, interferers from the mud pumps and noise affect the pressure wave propagation. This thesis provides a novel mathematical characterization of a mud communication channel and uses several signal processing techniques to enhance the performance of a mud pulse receiver. By introducing a fluid transmission line model, the attenuation of the pressure wave is characterised and is verified with the experimental results found in the literature. Based on this model, a transfer function of the mud communication channel including the effect of reflections from the multiple junctions has been derived. Finally, the receiver performance is evaluated by cancelling out the narrow-band interferers and equalizing the mud channel.