基于广义随机共振的Chirp信号检测性能分析

为便于提取多个chirp信号叠加噪声模型中目标chirp信号的参数信息，本文研究了该混合信号激励过阻尼双稳系统的随机共振现象。但由于chirp信号在频域能量的非聚焦性，传统刻画随机共振的信噪比指标失效。因此，基于chirp信号在分数阶傅里叶变换域上的能量分布特性，对非线性随机动力系统的畸变输出信号进行变换域上的最优滤波，给出最优分数阶傅里叶变换域上的信干比定义形式，并以此作为目标chirp信号经过系统后的性能增益的度量和广义随机共振现象的判别依据。数值仿真结果表明，在存在多个chirp信号驱动的过阻尼双稳系统中，当目标chirp信号或噪声能量不足以激发粒子跃迁时，干扰chirp信号能在一定程度上协助粒子发生跃迁，产生协同随机共振现象，从而提高对目标chirp信号的检测性能。

Chirp Signal Detection Performance Analysis Based on Generalized Stochastic Resonance

For estimating the parameter information of target chirp signal within multiple chirp signal and noise, which is the conventional familiar model in signal processing, the stochastic resonance (SR) in over-damped bistable system driven by the multiple signals and noise was investigated. However, because of the aperiodicity of chirp signal, conventional signal-to-noise ratio (SNR) defined in frequency domain became invalid. Therefore, using the energy aggregation on optimal fractional Fourier transform domain of chirp signals, the distorted output signals were filtered on optimal fractional Fourier transform (FrFT) domain, and a new signal-to-interference ratio (SIR) gain defined in optimal FrFT domain was proposed to describe the system performance, and used to observe the generalized SR phenomenon. The simulation results showed that interfering chirp signals could assist weak noise with particle jump, which was called coordinative SR phenomenon (CSR). Moreover, the detection performance of target chirp signal was improved.