1. A method of monitoring maternal and fetal vital signs of a maternal patient and a fetus, the method comprising the steps of: placing a plurality of electrodes on the abdomen of the maternal patient; obtaining a plurality of separate input waveforms from the maternal patient through the plurality of electrodes over a predetermined epoch; conducting an independent component analysis (ICA) on the input waveforms over the epoch to generate a plurality of ICA output waveforms; determining which of the ICA output waveforms is generated from a maternal signal source and which of the ICA output waveforms is generated from a fetal signal source; processing the ICA output waveform that includes a maternal ECG signal to generate physiological information for the maternal patient; and processing the ICA output waveform that includes a fetal ECG signal to generate physiological information for the fetus.