Ultra-wideband (UWB) signal processing is a technology that has tremendous potential to develop advances in communication and information technology. However, it also presents challenges to the signal processing community, and, in particular, to sampling theory. This article outlines a UWB signal processing system via a basis projection and a basis system designed specifically for UWB signals. The method first windows the signal and then decomposes the signal into a basis via a continuous-time inner product operation, computing the basis coefficients in parallel. The windows are key, and we develop windows that have variable partitioning length, variable roll-off and variable smoothness. They preserve orthogonality of any orthonormal system between adjacent blocks. In this paper, we develop new windows, and give an outline for a new architecture for the projection. We then use this projection with a basis system designed to work with UWB signals, implementing modified Gegenbauer functions designed specifically for these signals.