Aperiodic resonance of a nonlinear system excited by aperiodic binary signal or <i>M</i>-ary signal

Abstract

The aperiodic resonance of a typical nonlinear system that excited by a single aperiodic binary or <i>M</i>-ary signal and its measuring method are studied. The focus is on exploring aperiodic resonance caused by the system parameter. A response amplitude gain index suitable for aperiodic excitation is proposed to measure the effect of aperiodic resonance, and the research is carried out by combining the cross-correlation coefficient index and bit error rate index. The results show that the cross-correlation coefficient can better describe the synchronization and waveform similarity between the system output and the input aperiodic signal, but cannot describe the situation whether the signal is amplified after passing through the nonlinear system. The response amplitude gain can better describe the amplification of signal amplitude after passing through the nonlinear system, but cannot reflect the synchronization and waveform similarity between the system output and the input aperiodic signal. The aperiodic resonance occurs at the valley corresponding to the cross-correlation coefficient and the peak corresponding the response amplitude gain. The aperiodic resonance locations reflected on both the cross-correlation coefficient and the response amplitude gain curves are the same. The bit error rate can describe the synchronization between the system output and the input signal at appropriate thresholds, as well as the degree to which the aperiodic signal is amplified after passing through the nonlinear system. The bit error rate curve can directly indicate the resonance region of the aperiodic resonance. The aperiodic resonance can occur in a nonlinear system excited by a single aperiodic binary or <i>M</i>-ary signal, and its aperiodic resonance effect needs to be measured by combining the cross-correlation coefficient, response amplitude gain, bit error rate and other indices together.