Sharpened Gaussian Derivatives and Their Application in UWB Pulse Design

Gaussian derivatives are bandpass waveforms well localized in time. Consequently, they are often applied in the design of ultra-wideband (UWB) pulses. However, the efficiency of Gaussian derivatives in filling the UWB spectral mask is low. In this paper, we propose their modification which significantly increases this efficiency. The modification is based on a well-known technique called polynomial sharpening. To obtain high spectral efficiency, we sharp the magnitude spectrum of a Gaussian derivative with the Kaiser-Hamming polynomials. These polynomials impose flatness at spectrum's peak, while maintaining a good time localization. The proposed approach is illustrated with the design of UWB pulses that fill the FCC masks.