A binary bandpass communications system is considered, in which the ratio of bandwidth to intermediate frequency (IF) is not necessarily small. Closed-form expressions are given in the case when the receiver (IF) filter has

distinct poles. Explicit results, namely probabilities of error, are computed when the filter is a bandpass Butterworth filter. The effect of

(ratio of half filter bandwidth to IF),

(product of half filter bandwidth and bit duration),

, phase and time jitter on probability of error, is investigated.