Optimum (Wiener sense) filters for suppression of noise in multiple time series are computed by a new method due to E. A. Robinson. Filters for prediction error and interpolation error have been used to detect P-wave signals from three teleseismic events. These filters facilitate detection of signals in noise with low signal-to-noise ratios. The instrumentation consists of short-period Benioff seismometers, both three-component stations and surface arrays of verticals.It was found that microseismic noise in the pass band of these instruments is more accurately termed "Brownian motion of a surface" than "random waveforms with characteristic direction(s) of propagation". Thus, single time-series filters work almost as well as multiple time-series matrix filters. Prediction-error filters gave results substantially more satisfactory than simple band-pass filters.