  We report on Fourier spectroscopy experiments performed with near-surface
nitrogen-vacancy centers in a diamond chip. By detecting the free precession of
nuclear spins rather than applying a multipulse quantum sensing protocol, we
are able to unambiguously identify the NMR species devoid of harmonics. We
further show that by engineering different Hamiltonians during free precession,
the hyperfine coupling parameters as well as the nuclear Larmor frequency can
be selectively measured with high precision (here 5 digits). The protocols can
be combined to demonstrate two-dimensional Fourier spectroscopy. The technique
will be useful for mapping nuclear coordinates in molecules en route to imaging
their atomic structure.
