非周期二进制/M进制信号激励下非线性系统的非周期共振研究

Aperiodic resonance of a nonlinear system excited by aperiodic binary signal or M-ary signal

研究单一非周期二进制或M进制信号激励下一类非线性系统的非周期共振现象及其度量方法,重点探讨了系统参数引起的非周期共振.提出了适用于非周期共振度量的响应幅值增益指标,并结合互相关系数和误码率展开研究.结果发现,互相关系数能够较好地描述系统输出和输入信号之间的同步性及波形相似性但无法刻画信号通过系统后被放大的程度.响应幅值增益能够较好地描述信号通过系统后幅值被放大的程度,但无法反映系统输出和输入信号之间的同步性及波形相似性.非周期共振发生在互相关系数取谷值和响应幅值增益取峰值处,且两种指标曲线反映的共振点相同.误码率在合适的阈值下可以描述系统输出和输入信号之间的同步性以及非周期信号通过系统后被放大的程度,误码率曲线可以直接给出非周期共振的共振区.单一非周期二进制或M进制信号激励下的非线性系统可以发生非周期共振,其共振效果需要综合互相关系数、响应幅值增益、误码率等指标进行度量.

The aperiodic resonance of a typical nonlinear system that excited by a single aperiodic binary or M-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 M-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.