Sampling and Frame Expansions for UWB Signals

This article outlines sampling and frame expansions designed specifically for ultra-wideband (UWB) signals. We present two different types of expansions: ON windows with modified Gegenbauers and generalized frame expansions. They represent a contrast in the computability and flexibility of frames versus the rigid structure and precision in the sampling expansion. Both approaches rely on the multiplication of some super-windowing functions and given orthonormal sequences. We generalize this approach to the redundant case, investigating windowed families of frame sequences.