Antenna synthesis can yield optimal radiating structures in terms of pattern diagram, gain, bandwidth or other figures of merit. Although the synthesis might be more difficult for continuous sources than for antenna arrays the resulting radiating structures are cheaper and easy to manufacture. In this paper, we propose a time-domain synthesis approach for ultra-wide band antennas. The method is based on a finite expansion of the antenna time-domain response. The synthesis is performed with regard to the resemblance between the time-domain radiated waveform and the waveform at the antenna input. The approach is validated by synthesizing a planar, ultra-wide band antenna designed for a particular waveform of excitation.