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Through theoretical analysis and numerical simulation, this paper proves that the classical bistable system is existence of output saturation. When the system output reaches saturation, the output signal to noise ratio (SNR) will drop rapidly, and it's poor to extract a useful signal from the strong background noise. Therefore, we put forward a new piecewise hybrid system, and prove that there is no saturation in it. We studied on signal extraction of the system under the strong background noise. The research shows that the output SNR of our system is significantly higher than that of bistable system.