Ultra-wideband (UWB) radio utilizes very short pulses to transmit data. These pulses should efficiently fill a given spectral mask and be well concentrated in the time domain. Common UWB pulses exploit Gaussian derivatives. These derivatives are well concentrated in the time domain, but they do not exploit the area under the mask efficiently. In the dissertation, two methods for the design of spectrally and energy efficient pulses based on the Gaussian pulse and its derivatives are presented. The first method is based on sharpening of the magnitude spectrum of an arbitrary Gaussian derivative by applying the Kaiser-Hamming polynomials. Such sharpening offers controllable flatness at the top of the magnitude spectrum as well as controllable steepness in spectrum's transition regions. The second method is inspired by Gaussian derivatives, in which the Gaussian is weighted by Hermite polynomials. In the dissertation, optimum weighting polynomials are constructed, which ensure maximum flatness at the peak of pulse’s magnitude spectrum. Compared to other Gaussian-based waveforms, both methods bring the pulses with significantly higher spectral efficiency and only slightly lower energy concentration. The approximation of the ideal UWB waveforms by using impulse responses of continuous-time filters is also considered. The transfer functions of these filters suitable for shaping various conventional as well as the proposed UWB pulses are provided.