A non-linear parametric model for brain activation detection by functional magnetic resonance imaging (FMRI) is proposed. The effects of a designed temporal stimulus on the FMRI signal at each brain location in a 36×60 spatial grid are estimated from discrete Fourier transforms of the observed time series at each location. The frequency domain regression model accommodates unobservable and spatially varying haemodynamic response functions through their estimated convolutions with the global stimulus. This approach generalizes an existing method for human brain mapping. An experiment to detect focal cortical activation during primary visual stimulation demonstrates the usefulness of the method.