144 / 2025-06-02 17:17:56

Fundamental Limits of Stochastic Resonance for Completely Submerged Periodic Signal Detection

stochastic resonance,bistable system,detection of weak periodic signal,numerical simulation

Weak periodic signal detection is a critical issue in radar signal recognition, medical diagnosis, mechanical condition monitoring, and related fields. The stochastic resonance (SR) phenomenon in bistable systems has been extensively studied as a promising method to enhance detection capabilities under low signal-to-noise ratio (SNR) conditions. This paper systematically investigates the performance boundaries of conventional spectral analysis and SR-based methods through theoretical modeling, numerical simulations, and quantitative statistical analysis. First, the principles and influencing factors of spectral analysis for weak periodic signal detection are analyzed, with particular emphasis on the dominant role of sampling duration. Theoretical results demonstrate that any weak periodic signal can be identified through spectral analysis given sufficiently extended sampling time, as the spectral resolution improves inversely with temporal resolution. Subsequently, a frequency-domain hypothesis testing framework is established for discrete sampled signals in white noise environments, incorporating quantitative metrics such as local SNR and F-distributed detection statistics to objectively evaluate detection efficacy. Comparative studies reveal that the SR method exhibits no significant advantage over direct spectral analysis when detecting completely submerged signals. Numerical simulations show that when the input signal spectrum fails to display discernible periodic features due to high noise intensity, the output spectrum of the bistable SR system similarly cannot highlight the target frequency component. Quantitative simulation results indicate a detection rate difference of less than 3% between the two methods across varying noise intensities (2≤D≤50). Further mechanistic analysis clarifies that SR fundamentally relies on the weak dominance of the target frequency component in the input spectrum. The energy conversion mechanism requires the periodic signal to maintain a minimal local advantage over adjacent noise components; otherwise, effective resonance cannot be triggered. This study explicitly delineates the limitations of SR in scenarios where signals are entirely submerged by noise, providing critical boundary conditions for its engineering applications. Notably, SR demonstrates potential advantages in time-domain waveform enhancement, particularly for signals with intermittent or non-stationary characteristics. The proposed hypothesis testing framework and quantitative evaluation methodology may further facilitate standardized comparisons of emerging detection algorithms in future research.