Improving the weak aperiodic signal by three kinds of vibrational resonance

The aperiodic vibrational resonance (VR) is investigated in a typical nonlinear system with fractional-order deflection. The character signal used to express the useful information is an aperiodic binary signal. The informationless auxiliary signal used to induce VR is of a square waveform. We study the classic aperiodic VR at first. If the strength of the auxiliary signal is a control parameter, we find that the value and the location of the resonance peak on the cross-correlation coefficient curve are independent of the fractional-order exponent. However, for a smaller value of the fractional-order exponent, the aperiodic signal can be improved to a greater extent. Moreover, if the minimal random pulse width of the aperiodic signal is small, the classic aperiodic VR cannot occur. We propose two methods to solve this problem. The first one is the re-scaled aperiodic VR method in which the scale parameter is the key factor. The second one is the twice sampling aperiodic VR method in which the sampling transform ratio is the key factor. Through some examples, we verify the validity of the two proposed methods. By the two methods, we can improve the aperiodic signal with an arbitrary minimal random pulse width. Further, the methods proposed in this paper not only can improve the aperiodic bipolar binary signal, but also can deal with other kinds of signals.