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Weak signal detection via stochastic resonance (SR) has attracted considerable attention in a wide range of research fields, especially under heavy background noise circumstances. In this paper, a second-order matched stochastic resonance (SMSR) method is proposed to further improve the signal-to-noise ratio of weak period signal. By selecting a proper damping factor in the regime of second-order parameter matched relationship, weak periodic signal, background noise, and nonlinear system can be matched in generating an enhanced output. The matched relationship is deduced in combining noise intensity optimization and signal frequency synchronization with duffing system in a mathematical way, and a normalized scale transformation is further carried out to make it accessible in detecting arbitrary high frequency signals. The numerical analysis and application verification are performed to confirm the validity and effectiveness of theoretical results, which indicate the proposed SMSR method is superior to the first-order parameter matched stochastic resonance in achieving a good band-pass filtering effect with a low-noise output as the driving frequency of received signal is not too small (&#x2265;0.1 Hz). Thus, the proposed method is beneficial to practical engineering weak signal processing and anticipates to be a potential novel technique for ship radiated line-spectrum detection.

Effects of Second-Order Matched Stochastic Resonance for Weak Signal Detection