  Super-resolution theory aims to estimate the discrete components lying in a
continuous space that constitute a sparse signal with optimal precision. This
work investigates the potential of recent super-resolution techniques for
spectral estimation in multi-rate sampling systems. It shows that, under the
existence of a common supporting grid, and under a minimal separation
constraint, the frequencies of a spectrally sparse signal can be exactly
jointly recovered from the output of a semidefinite program (SDP). The
algorithmic complexity of this approach is discussed, and an equivalent SDP of
minimal dimension is derived by extending the Gram parametrization properties
of sparse trigonometric polynomials.
