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A new optimal waveform for Ultra-wideband (UWB) radios is proposed in this paper. This new waveform extracted through mathematical analysis for achieving high spectral utilization under the restrictions imposed by the U.S. Federal Communications Commission (FCC) spectral masks. Exploiting Inverse Fourier Transform (IFT) of FCC mask, the required analog signals are extracted through robust calculation and the optimum realizable analog signal for FCC mask is constructed while the simulations confirmed the analytical approach. Normalized effective signal power (NESP) of the proposed method is 95.27% which shows better efficiency compared to the other methods in the literature.