Minimal identification of sums of exponentials with unknown parameters

Abstract 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>2</m:mn> <m:mo>⁢</m:mo> <m:mi>N</m:mi> </m:mrow> </m:math> {2N} 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.