  Gravitational waves modulate the apparent frequencies of other periodic
signals. Low-frequency gravitational waves could therefore be detected by
observing frequency modulations in signals from higher-frequency sources, e.g.,
those from binary white dwarfs detected with the LISA gravitational-wave
detector. We propose a concrete method to extract these modulations by
coherently adding the cross-spectra of a large number of well-resolved
quasi-monochromatic signals. We apply this method to the case of LISA, and find
this method would enable the detection of background gravitational wave strain
amplitudes of, e.g., $A\simeq10^{-10}$ at a frequency $F\simeq10^{-8}\,\rm Hz$,
given current projections for the number and properties of Galactic binary
white dwarfs and the sensitivity of the instrument. We also estimate (to within
an order of magnitude) that this method could potentially compete with that of
current Pulsar Timing Arrays when using signals from binary neutron stars such
as those expected to be observed with proposed detectors like DECIGO. Our
results show that gravitational-wave detectors could be sensitive at
frequencies outside of their designed bandwidth using the same infrastructure,
which has the potential to open up unexplored and otherwise inaccessible parts
of the gravitational wave spectrum.
