  Many real life problems can be reduced to the solution of a complex
exponentials approximation problem which is usually ill posed. Recently a new
transform for solving this problem, formulated as a specific moments problem in
the plane, has been proposed in a theoretical framework. In this work some
computational issues are addressed to make this new tool useful in practice. An
algorithm is developed and used to solve a Nuclear Magnetic Resonance
spectrometry problem, two time series interpolation and extrapolation problems
and a shape from moments problem.
