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The authors present a constraint formulation that yields a real-numbered solution to the frequency-domain Prony algorithm. This is done by requiring that all the roots of the Z-transform of the solution be on the unit circle. They make appropriate transformations that map this unit circle onto a left half plane, which then allows them to use Sturn's theorem to check the number of roots in the left half plane. This newly formulated constraint is incorporated in the Prony method in the frequency domain. One of the applications of the method is in the decomposition of a mixture of delayed versions of a signal, where the constraints guarantee that the solution for the time delays are real.< >