Objective: Here, we review the theory of suppression of spatially uncorrelated, sensor-specific noise in electro- and magentoencephalography (EEG and MEG) arrays, and introduce a novel method for suppression. Our method requires only that the signals of interest are spatially oversampled, which is a reasonable assumption for many EEG and MEG systems. Methods: Our method is based on a leave-one-out procedure using overlapping temporal windows in a mathematical framework to project spatially uncorrelated noise in the temporal domain. Results: This method, termed “oversampled temporal projection” (OTP), has four advantages over existing methods. First, sparse channel-specific artifacts are suppressed while limiting mixing with other channels, whereas existing linear, time-invariant spatial operators can spread such artifacts to other channels with a spatial distribution which can be mistaken for one produced by an electrophysiological source. Second, OTP minimizes distortion of the spatial configuration of the data. During source localization (e.g., dipole fitting), many spatial methods require corresponding modification of the forward model to avoid bias, while OTP does not. Third, noise suppression factors at the sensor level are maintained during source localization, whereas bias compensation removes the denoising benefit for spatial methods that require such compensation. Fourth, OTP uses a time-window duration parameter to control the tradeoff between noise suppression and adaptation to time-varying sensor characteristics. Conclusion: OTP efficiently optimizes noise suppression performance while controlling for spatial bias of the signal of interest. Significance: This is important in applications where sensor noise significantly limits the signal-to-noise ratio, such as high-frequency brain oscillations.