离散时间系统中随机谐振研究

Stochastic Resonance Research of a Discrete-time System

基于一种新的信噪比的定义讨论了在四种经典噪声下在离散时间系统中的随机谐振现象。当输入信号是阈上信号时,噪声总是在恶化信号的传输,即随着噪声强度增加,输出信噪比呈现单调递减的趋势。然而当输入信号是阈下信号时,适当的噪声能够引起系统最优反应,即随着噪声强度的增加,输出信噪比达到一个最大峰值,也即存在明显的随机谐振现象。随着非线性系统中阈值的增加,随机谐振现象的明显度降低,当最佳噪声强度在增加时,输出信噪比的最优值却在减少。文中结果也说明,基于新的信噪比的定义是可以用来度量一个离散时间系统的随机谐振现象,且随机谐振对噪声具有一定的鲁棒性,拓广了随机谐振在信息传输领域的应用。

Based on a new signal-to-noise ratio （ SNR ）, a study is made on stochastic resonance of a discrete-time system under four rep resentative noise. When the input signal is supra-threshold, the noise is always in the inhibition of signal transmission, that is, with in- creasing noise intensity, the output SNR presents a monotonically descreasing trend. However, when the input signal is subthreshold sig- nals,appropriate noise can cause the best response of the system,namely with the increase of noise intensity,the output SNR reaches a maximum peak, the existence of stochastic resonance phenomenon. With the increase of the threshold in the nonlinear system, the stochas tic resonance phenomenon apparently reduced when the optimal noise intensity increased, the optimal value of the output SNR is decrea sing. The results in this paper show that based on the new SNR is defined as the stochastic resonance phenomenon can be used to measure a discrete-time system, and stochastic resonance has a certain robustness to noise, extension of stochastic resonance in the field of infor- mation transmission.