Ultra-high-density EEG: How many bits of resolution do the electrodes need?

How much resolution do EEG electrodes need? We observe that as a consequence of the decay of EEG´s high spatial frequencies, one needs to extract small high spatial frequency signals that are added to large low spatial frequencies. This requires high dynamic range and low noise from the sampling circuitry. Using simplistic spherical-head models, we provide information-theoretic bounds on the number of bits of resolution that the Analog-to-Digital Converters for EEG systems require to extract high spatial frequencies (as a function of the highest spatial frequency recovered), which also specifies the required signal-to-noise ratio (SNR) from these electrodes.