The characteristics of Lorentzian distribution in the power spectrum of a stochastic resonance(SR) from a bistable system have been investigated, and then the viewpoint of producing an identifiable SR peak only at the lower frequency area where the power energy being concentrated has been proposed. With big values of parameters, the spectral properties of a twice sampling stochastic resonance(TSSR) from a bistable system is probed in detail. Take the detection of a weak signal overwhelmed in heavy noise as an example, the application of the TSSR technique is shown finally.