Magnetoencephalography (MEG) is a brain imaging technique that non-invasively measures neurallygenerated magnetic fields. Earlier MEG studies have focused on the neural responses to amplitude modulated (AM) auditory signals near 40Hz. Speech signals, however, contain a wide range of modulation rates, most of which are well below 40 Hz. Therefore we seek to characterize the modulation transfer function (MTF) of the human brain at AM frequencies much lower than 40Hz. The present study uses MEG to measure neural responses to pure-tone carrier signals amplitude modulated at frequencies exponentially fluctuating between 3Hz and 60Hz. Analysis of the neural MEG data includes noise reduction, timefrequency analysis to characterize the MTF, and a comparison to the neural response to constant AM stimuli. The maximal neural response was evident at low rate modulations, with the shape of the MTF following that of a shallow low-pass filter. The phase of the neural response was linear, consistent with an 80 ms delay. Neural phase responses to upward and downward sweeps differed by ~π radians for AM frequencies 15-35 Hz. An exponential AM chirp gave a successful estimate of the neural power MTF, closely matching that of the response to constant AM stimuli.