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The assessment of imperfect channels in data transmission usually involves noise considerations. Channel imperfections are related to system performance by determining the increase in carrier-to-noise ratio required to maintain a fixed error rate. The impairment is determined by examining the "eye" pattern, which shows the effective reduction in signal amplitude caused by intersymbol interference. This paper derives the eye function for the binary quadratic receiver. The binary instantaneous frequency discriminator, the differential phase shift receiver, and the noncoherent frequencyshift keying (FSK) receiver implemented using the difference of two envelopes are binary quadratic receivers. The eye pattern is easily obtained by computation using the eye function.