The design of data-adaptive filters requires that the noise be defined, statistically or otherwise, by parameters which allow some means of separating the noise from the signal. We consider here multichannel data in which one knows only that the noise is less polarized than the signal in a unitary space. This description of the noise is not sufficient for designing filters which are optimum in any sense; consequently, the filters may require a number of changes in the parameters before a satisfactory design can be found. Once this design has been achieved, the filters can be used to enhance waveforms of arbitrary shape, requiring little prior knowledge of the spectral content or temporal features of the signal. In contrast to many other data-adaptive filters which give a scalar time-series output, the filters we describe here with vector time series input have an equal number of input and output channels. A number of examples of filtered magnetic and seismic data are given in order to emphasize the wide range of uses for the filters. Some suggestions for application of the filters to multichannel seismic data are given.