Cognitive Radios (CR) can recognize the communication environment and switch its communication scheme to more efficiently and flexibly utilize the radio spectrum. The performance of ultra wideband (UWB) degrades if interference is not suppressed properly. We propose here a series of adaptive chirp waveforms in UWB systems. By designing waveform shaping of both linear chirp and non-linear cases, we avoid the estimated spectrum of the on-going applications without the necessity of notch filters, and thus reduce the system complexity. We evaluate system performance of the proposed scheme by simulations and verify that the proposed scheme is a candidate for cognitive UWB systems.