The impact of narrowband interference (NBI) on two ultra wideband (UWB) systems is analyzed. The two systems are impulse radio (IR) and a variation of it, termed direct-sequence IR (DS-IR). The signal-to-noise ratio (SNR) at the decision device of a correlation receiver is computed for both systems, assuming that the NBI is wide sense stationary and that the channel is frequency-selective. The SNR is expressed by means of a simple equation involving the signal and the interference spectrum. Next, a statistical model for the interference is introduced, considering the interference as the sum of a given number of sinusoidal signals with random powers and frequencies. The bit-error rate of IR and DS-IR is derived. The results are then specialized and compared with simulations in three case studies of practical interest, where the NBI is a single jammer with deterministic power and frequency, a multitone signal with random frequencies, or a grid of interfering signals with random powers.