  We describe a new technique for removing troublesome interference from
external coherent signals present in the gravitational wave spectrum. The
method works when the interference is present in many harmonics, as long as
they remain coherent with one another. The method can remove interference even
when the frequency changes. We apply the method to the data produced by the
Glasgow laser interferometer in 1996 and the entire series of wide lines
corresponding to the electricity supply frequency and its harmonics are
removed, leaving the spectrum clean enough to detect possible signals
previously masked by them. We also study the effects of the line removal on the
statistics of the noise in the time domain. We find that this technique seems
to reduce the level of non-Gaussian noise present in the interferometer and
therefore, it can raise the sensitivity and duty cycle of the detectors.
