The discrete sampling of the brain's electrical field at the scalp surface with individual recording sensors is subject to the same sampling error as the discrete sampling of the time series at anyone sensor with analog-to-digital conversion. Unlike temporal sampling, spatial sampling is intrinsically discrete, so that the post hoc application of analog anti-aliasing filters is not possible. However, the skull acts as a low-pass spatial filter ofthe brain's electrical field, attenuating the high spatial frequency information. Because of the skull's spatial filtering, a discrete sampling of the spatial field with a reasonable number of scalp electrodes is possible. In this paper, we provide theoretical and experimental evidence that adequately sampling the human electroencephalograph (EEG) across the full surface of the head requires a minimum of 128 sensors. Further studies with each of the major EEG and event-related potential phenomena are required in order to determine the spatial frequency of these phenomena and in order to determine whether additional increases in sensor density beyond 128 channels will improve the spatial resolution of the scalp EEG.When the time series ofan electroencephalogram (EEG) channel is sampled discretely, the Nyquist theorem specifies that the highest measurable frequency is half the sampling rate. For example, with a 250 sample/sec analog-to-digital conversion rate, the highest frequency that can be resolved is 125 Hz. In actuality, because of phase alignment, it is necessary to discretely sample (digitize) the signal at a rate at least 2.5 times the highest frequency component ofthe signal (Bendat & Piersol, 1986). Signal frequencies higher than the Nyquist frequency are not only poorly characterized; they alias or appear misleadingly as increased energy at lower frequencies. To avoid aliasing, it is necessary to eliminate the frequency components of the signal that are higher than the Nyquist frequency through analog filtering.The electrical field of the brain generates a potential distribution that is continuous over the surface of the head. The discretization ofthis spatial EEG or averaged eventrelated potential (ERP) signal with scalp electrodes is also subject to the Nyquist theorem. Ifthe spatial sampling is Correspondence concerning this article should be addressed to D. M.Tucker, Electrical Geodesics, Inc., Riverfront Research Park, 1811 Garden Avenue, Suite 104, Eugene, OR 97403 (e-mail: dtucker@egi.com).Note: ElectricalGeodesics, Inc. sells 64-, 128-,and 256-channelEEG systems and thus has a commercial interest in promoting dense sensor array technology.-Editor