  In this paper, motivated by diffraction of traveling light waves, a simple
mathematical model is proposed, both for the multivariate super-resolution
problem and the problem of blind-source separation of real-valued exponential
sums. This model facilitates the development of a unified theory and a unified
solution of both problems in this paper. Our consideration of the
super-resolution problem is aimed at applications to fluorescence microscopy
and observational astronomy, and the motivation for our consideration of the
second problem is the current need of extracting multivariate exponential
features in magnetic resonance spectroscopy (MRS) for the neurologist and
radiologist as well as for providing a mathematical tool for isotope separation
in Nuclear Chemistry. The unified method introduced in this paper can be easily
realized by processing only finitely many data, sampled at locations that are
not necessarily prescribed in advance, with computational scheme consisting
only of matrix - vector multiplication, peak finding, and clustering.
