Frequency-based detector for improved resolvability of closely-spaced exponential signals

In this paper, we introduce a new local frequency-based detector for improved resolvability of closely-spaced exponential signals. The frequency resolution problem is defined as a hypothesis-testing problem in the frequency domain, and a corresponding detector, based on the generalized likelihood ratio test is constructed. We derive a theoretical resolution limit in terms of the signal-to-noise ratio, the observable-data length, and the probabilities of detection and false-alarm. Experimental results validate the theoretical results and demonstrate the effectiveness of the proposed detector over a time-based detector.