Stochastic resonance (SR), a phenomenon originally introduced in climate modeling, enhances signal detection by leveraging optimal noise levels within non-linear systems. Traditional SR techniques, mainly based on single-threshold detectors, are limited to signals whose behavior does not depend on time. Often large amounts of noise are needed to detect weak signals, which can distort complex signal characteristics. To address these limitations, this study explores multi-threshold systems and the application of SR in multiscale applications using wavelet transforms. In the multiscale domain signals can be analyzed at different levels of resolution to better understand the underlying dynamics. We propose a double-threshold detection system that integrates two single-threshold detectors to enhance weak signal detection. We evaluate it both in the original data domain and in the multiscale domain using simulated and real-world signals and compare its performance with existing methods. Experimental results demonstrate that, in the original data domain, the proposed double-threshold detector significantly improves weak signal detection compared to conventional single-threshold approaches. Its performance is further improved in the frequency domain, requiring lower noise levels while outperforming existing detection systems. This study advances SR-based detection methodologies by introducing a robust approach to weak signal identification, with potential applications in various disciplines.

翻译：随机共振（SR）这一现象最初在气候建模中提出，它通过利用非线性系统中的最佳噪声水平来增强信号检测。传统的随机共振技术主要基于单阈值检测器，仅适用于行为不随时间变化的信号。检测微弱信号通常需要大量噪声，这可能扭曲复杂的信号特征。为克服这些局限性，本研究探索了多阈值系统以及基于小波变换的多尺度应用中随机共振的实现。在多尺度域中，信号可在不同分辨率层级上进行分析，以更好地理解其潜在动态特性。我们提出了一种双阈值检测系统，该系统通过集成两个单阈值检测器来增强微弱信号检测能力。我们分别在原始数据域和多尺度域中使用仿真信号与实际信号对该系统进行评估，并将其性能与现有方法进行比较。实验结果表明：在原始数据域中，所提出的双阈值检测器相较于传统单阈值方法显著提升了微弱信号检测性能；在频域中其性能得到进一步改善，仅需更低噪声水平即可超越现有检测系统。本研究通过引入一种鲁棒的微弱信号识别方法，推进了基于随机共振的检测方法论发展，在各学科领域均具有潜在应用价值。