Contrast response functions (CRFs) for the VEP were obtained with a Discrete Fourier Transform (DFT) technique employing swept contrast gratings. VEP CRFs in infants were found to have a form similar to those observed in adults, being linear functions of log contrast over a range of near-threshold contrasts. CRFs with low and high contrast lobes were present in infants, as they are in adults. Contrast thresholds were estimated by extrapolation of the CRF to zero microvolts. The effects of additive EEG noise and of the DFT data window on the shape of the measured CRF are considered. For large signals, the measured CRF is nearly independent of the additive noise, but at small signal values additive noise introduces a small bias towards larger amplitudes. The VEP signal-plus-noise distribution was modeled as a family of Rice distributions in order to evaluate the effects of bias on the estimates of threshold. The amount of bias depends inversely upon the slope of the CRF. The amount of bias introduced by a smoothing window also depends upon slope of the CRF as well as the sweep rate. The combined effects of additive noise and window bias were such that the total bias was nearly independent of CRF slope. Sweep VEP contrast thresholds were shown empirically to be unaffected by changes in the range of contrast swept.