The performance of an optimum filter is analyzed and compared to that of a whitening filter and a conventional matched filter for rejecting interference in spread spectrum systems. It is shown that the performance analysis of the optimum filter can be greatly simplified by formulating the detection process in the discrete-time domain and modeling the noise as a Markov process. In this formulation, the relative processing gain of the optimum filter over other types of filter can be easily calculated and the effect of filtering operations on inter-symbol interference can be clearly demonstrated. Specifically, closed form expressions for the filter performance in the presence of interference is derived for a BPSK spread spectrum system.