一种分数阶随机共振系统的弱信号检测研究  

The Research of Weak Signal Detection Based on a Fractional Stochastic Resonance System

作　　者：张刚[1] 宋莹[1] 张天骐[1] 

机构地区：[1]重庆邮电大学信号与信息处理重庆市重点实验室,重庆400065

出　　处：《科学技术与工程》2016年第4期210-215,共6页Science Technology and Engineering

基　　金：国家自然科学基金项目(61371164);重庆市杰出青年基金项目(CSTC2011jjjq40002);重庆市自然科学基金项目(CSTC2012JJA40008);重庆市教育委员会科研项目(KJ130524)资助

摘　　要：在利用随机共振系统进行弱信号检测的研究中大多是以整数阶朗之万方程为主,针对分数阶随机共振的鲜有研究。对过阻尼分数阶朗之万方程的随机共振特性进行深入研究分析,对于分数阶朗之万方程求解这一难题,引入Oustaloup算法对其近似化,搭建分数阶朗之万方程的近似仿真模型,找出了产生随机共振的阈值,实现了对满足绝热近似理论的微弱信号的检测,且讨论了不同分数阶阶次和噪声强度对分数阶朗之万方程产生随机共振的影响。数值分析表明,在一定阶数时,分数阶朗之万方程可以产生随机共振,且对微弱信号的检测及放大效果明显好于整数阶。该研究拓展了朗之万方程随机共振的研究范围,在信号检测与处理以及通信领域有着重要的应用价值。Most of the research of weak signal detection Langevin equation. The characteristics of stochastic resonance depending on stochastic resonance （SR） are integer （SR） system based on over-damped fractional Lange- vin equation （FLE） is deeply studied for a small amount of research of fractional stochastic resonance. For solving FLE, Oustaloup algorithm are introduced for its approximation. The threshold of the stochastic resonance has been found, and the weak signal detection has been achieved which meets the adiabatic approximation theory. In addi- tion, the effects of fractional order and noise intensity on FLE are studied respectively. The numerical simulation re- sults show that in a certain range of the order, FLE can generate stochastic resonance, and it is evident that the SNR gain in fractional Langevin equation is better than that in the integer order situation. The study has important practical potential in the field of weak signal detection, processing and communication, which expands the research scope of stochastic resonance based on Langevin equation.

关 键 词：分数阶微积分 朗之万方程 Oustaloup算法 随机共振 

分 类 号：TN391.9[电子电信—物理电子学]