  The problem of estimating the frequencies of an exponential sum has been
studied extensively over the last years. It can be understood as a sparse
estimation problem, as it strives to identify the sparse representation of a
signal using exponentials. In this paper, we are interested in its intrinsic
stability properties. We derive a bound very similar to the restricted isometry
property. Conditional well-posedness follows: Any exponential sum with samples
close to the unknown ground truth has close frequencies as well, provided that
it satisfies our model assumptions. The most important assumption is that the
frequencies are well-separated. Furthermore, we show that the presented bound
is sharp and gives rise to improved estimates of condition numbers of certain
Vandermonde matrices.
