The effects of limited frequency bandwidth on the response of space- integrating acousto-optic correlators are considered. They are studied in the classical scope of pseudorandom sequence correlation, used in spread spectrum systems, in terms of the SNR enhancement in the correlator compared to the ideal (infinite bandwidth correlator) enhancement figure. An analytical approach using filtering of both useful signals and noise at the correlator input is developed. Numerical computations are drawn that show a loss of 4 dB when the code chip rate used is equal to three times the correlator bandwidth. Experimental results obtained for an acousto-optic cell are also presented and agree well with the theoretical results.