Design of smooth ultra wideband pulses exploiting non-orthogonal properties of the Hermite pulses

This paper describes a method for designing smooth ultra wideband pulses that can efficiently fit symmetric (with respect to a central frequency) spectrum masks. This method relies on the fact that the sum of continuous functions is continuous and the time and frequency characteristics of the Hermite pulses. We show that the nth Hermite pulse spectrum can be discretized into n + 1 sub-bands and, to some extent, control their individual amplitudes without losing the softness of its time domain counterpart. However, Hermite pulses spectrum occupancy is not optimal because of zeros in their spectrum, therefore, we further propose to combine two different spectrum-modified Hermite pulses to achieve smooth and spectrum efficient UWB pulses for single-pulse ultra wideband applications.