I present a new method for removing unwanted components from neurophysiological recordings such as magnetoencephalography (MEG), electroencephalography (EEG), or multichannel electrophysiological or optical recordings. A spatiotemporal filter is designed to partition recorded activity into noise and signal components, and the latter are projected back to sensor space to obtain clean data. To obtain the required filter, the original data waveforms are delayed by a series of time delays, and linear combinations are formed based on a criterion such as reproducibility over stimulus repetitions. The time shifts allow the algorithm to automatically synthesize multichannel finite impulse response filters, improving denoising capabilities over static spatial filtering methods. The method is illustrated with synthetic data and real data from several biomagnetometers, for which the raw signal-to-noise ratio of stimulus-evoked components was unfavorable. With this technique, components with power ratios relative to noise as small as 1 part per million can be retrieved.