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In this paper, we present designs for a microstrip line UWB monopole antenna and a CPW fed UWB monopole antenna. First, a monopole antenna to cover the entire UWB band of 3.1-10.6GHz is designed. Different types of tapers are investigated to achieve the impedance match over the desired band. Next, two band-rejection notches at 5.2GHz and 5.8GHz are introduced by combining two traditional band-notching techniques. Performance of the proposed antennas has been investigated in both frequency and time domain. It is found that the antennas exhibit omnidirectional radiation in H-Plane, with a gain of 2-4dB except at the notch frequencies. Both antennas also exhibit low-level ringing and pulse distortion, making them suitable for applications in UWB communication systems.