Resolution of closely spaced deterministic signals with given success rate

Fundamental limitations on estimation accuracy are well known and include a variety of lower bounds including the celebrated Cramer Rao Lower Bound. However, similar theoretical limitations on resolution have not yet been presented. We exploit results from detection theory for deriving fundamental limitations on resolution. The results are general and are not based on any specific resolution technique and therefore hold for any method and for any resolution success rate. We show that for signals with additive white Gaussian noise the resolution is given by a simple expression related to signal to noise ratio, the signals waveforms and the resolution success rate. As an example, we discuss the resolution of two sinusoids with closely spaced frequencies. The result is compared with the empirical performance of the Akaike information criterion, and the Minimum Description Length criterion for model order selection.