It is believed that spatial summation in most simple cells is a linear process. If this were so, then the Fourier transform of a simple cell's line weighting function should predict the cell's spatial frequency tuning curve. We have compared such predictions with experimental measurements and have found a consistent discrepancy: the predicted tuning curve is much too broad. We show qualitatively that this kind of discrepancy is consistent with the well-known threshold nonlinearity shown by most cortical cells. We have tested quantitatively whether a response threshold could explain the observed disagreements between predictions and measurements: a least-squares minimization routine was used to fit the inverse Fourier Transform of the measured frequency tuning curve to the measured line weighting function. The fitting procedure permitted us to introduce a threshold to the reconstructed line weighting function. The results of the analysis show that, for all of the cells tested, the Fourier transforms produced better predictions when a response threshold was included in the model. For some cells, the actual magnitude of the response threshold was measured independently and found to be compatible with that suggested by the model. The effects of nonlinearities of spatial summation are considered.