  Sampling a signal below the Shannon-Nyquist rate causes aliasing, meaning
different frequencies to become indistinguishable. It is also well-known that
recovering spectral information from a signal using a parametric method can be
ill-posed or ill-conditioned and therefore should be done with caution.
  We present an exponential analysis method to retrieve high-resolution
information from coarse-scale measurements, using uniform downsampling. We
exploit rather than avoid aliasing. While we loose the unicity of the solution
by the downsampling, it allows to recondition the problem statement and
increase the resolution.
  Our technique can be combined with different existing implementations of
multi-exponential analysis (matrix pencil, MUSIC, ESPRIT, APM, generalized
overdetermined eigenvalue solver, simultaneous QR factorization,...) and so is
very versatile. It seems to be especially useful in the presence of clusters of
frequencies that are difficult to distinguish from one another.

Numerical Analysis