中文摘要：

根据Kramers逃逸速率的特性，阐明了随机共振信号的频率被限制在Kramers逃逸速率极限值一半的范围内，这种限制是制约大频率信号产生随机共振的原因．在进一步揭示二次采样随机共振频率尺度变换机理的基础上，证明了二次采样频率尺度可以把任意信号频率映射变换到随机共振频率尺度上的结论．相对于二次采样变换方法，由于双稳系统参数的调节很难使Kramers逃逸速率的一半达到实际信号的大频率，因此系统参数只能在随机共振的小参数频率范围内调节来实现随机共振．

英文摘要：

Kramers rate restricts the stochastic resonance （SR） frequency within the scope of half of its limit value. This restriction is the cause of SR failure of high frequency signal. By revealing the mechanism of frequency transformation of the twice sampling SR, we prove that the frequency scale ratio of the twice sampling SR can map or transform any signal frequency to the SR frequency scale. Compared with the method of twice sampling SR, the approach of adjusting system parameters to realize SR can only be used within the small SR frequency range, since in tuning bistable system parameters it is hard to make half the Kramers rate equal to the high frequency of the real signal.