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.