Abstract
We propose the piecewise re-scaled vibrational resonance (VR) method and the piecewise twice sampling VR method to amplify the weak linear frequency-modulated (LFM) signal. The system used to amplify the weak LFM signal is a typical bistable system with fractional-order deflection nonlinearity. The concrete procedures of both the piecewise re-scaled VR method and the piecewise twice sampling VR method are explained in detail. Through studying the effect of the factional-order exponent on VR, we find that the traditional bistable system is not the optimal model to improve the weak LFM signal. By investigating different parameters on the VR phenomenon, we verify the effectiveness of the two proposed methods.
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