On the resolvability of sinusoids with nearby frequencies in the presence of noise

This correspondence develops statistical algorithms and performance limits for resolving sinusoids with nearby frequencies in the presence of noise. We address the problem of distinguishing whether the received signal is a single-frequency sinusoid or a double-frequency sinusoid, with possibly unequal, and unknown, amplitudes and phases. We derive a locally optimal detection strategy that can be applied in a standalone fashion or as a refinement step for existing spectral estimation methods to yield improved performance. We further derive explicit relationships between the minimum detectable difference between the frequencies of two tones for any particular false alarm and detection rate and at a given SNR.