Fundamental Limitations on the Resolution of Deterministic Signals

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 limit is approximated by a simple expression related to the signal to noise ratio, the signal waveform and the resolution success rate. As an example, we discuss the resolution of two complex exponentials with closely spaced frequencies. The theoretical result is compared with the empirical performance of model order selection methods such as the Akaike information criterion and the minimum description length.