In this paper we demonstrate the usefulness of an eigenvector based spatial filtering method for signal processing of multi-channel fetal magnetocardiogram (fMCG) and fetal magnetoencephalogram (fMEG) recordings. This method of filtering can separate signal and interference by exploiting the considerable spatial information contained in multi-channel recordings. Typically, fMCGs and fMEGs suffer from large cardiac interference and low signal-to-noise ratio. To isolate the signal from the interference, we identify their respective subspaces using one portion of the record dominated by the signal and another dominated by the interference. Each subspace is approximately rank two since the sources of the signal and interference can be modeled as current dipoles. The spatial filter consists of a linear transformation that preserves the signal subspace and annihilates the interference subspace. It is easier to implement than a matched filter, preserves the morphology and topography of the fetal signal, and effectively removes maternal cardiac interference, even when the maternal and fetal complexes overlap strongly in time or when small maternal movements or maternal arrhythmias alter the temporal character of the interference.