Minimal identification of sums of exponentials with unknown parameters

Sums of real and complex exponentials are ubiquitous in mathematics. Given an arbitrary linear combination of N exponentials, in this paper we demonstrate how the unknown parameters in the exponents and the coefficients of this series may be obtained from sampled values of the function at arbitrary 2⁢N points. This result provides an alternative, more refined, solution to the De Prony problem (1795), where the latter is based on a finite difference scheme and requires uniform sampling.