Ultra-wideband (UWB) signal processing is a technology with many features that could develop into advances in communication and information technology. The technology has tremendous potential, but also presents challenges to the signal processing community, and, in particular, to sampling theory. UWB systems require either rapidly changing or very high sampling rates. Conventional analog-to-digital devices have limited dynamic range. This motivates rethinking how one could reliably sample a UWB signal. 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 UWB signals. The Gegenbauer system minimizes the Gibbs phenomenon. This gives the point values of a piecewise smooth signal with essentially the same accuracy as a smooth approximation, making it the ideal system to use for UWB systems.
Sampling Theory and Applications, 12th International Conference,
July 3 7, 2017,
and Casey, S.
Sampling Architectures for Ultra-Wideband Signals, Sampling Theory and Applications, 12th International Conference,
July 3 7, 2017,, Tallinn,, -1, [online], https://doi.org/10.1109/SAMPTA.2017.8024452
(Accessed September 30, 2023)