振动调频信号的时延二次变换解调研究

调频信号在频谱上具有与调幅信号相同的频率分布特征，然而，轴承和齿轮故障诊断中常用的解调方法却只适用于调幅信号，不能分析调频信号。基于以上问题，从确定调频信号频率分量幅值的贝塞尔函数的性质出发，分析了平方解调法不能对调频信号进行解调的原因。分析过程中发现由于贝塞尔函数的一些特殊性质，使得常用的解调方法不再适用于调频信号。针对这个原理，本文提出利用时延二次变换（信号与时延信号的乘积）打破调频信号边频分量的贝塞尔函数的特殊性，使得变换之后的信号中包含有调制频率，从而实现了对调频信号的解调。

FREQUENCY DEMODULATION BASED ON TIME LAG QUADRATIC TRANSFORM

The demodulation analysis is extensively used in fault diagnoses of gears and bearings.However,the current demodulation methods mainly aim to amplitude modulation(AM).Although the frequency modulation(FM)signal can be expressed as the sum of harmonics,it can not be demodulated by these methods.Here,the relationship between the sidebands of FM signals and Bessel function is studied carefully.The amplitude of sidebands of FM signals is totally determined by using the Bessel function is studied carefully.The amplitude of sidebands of FM signals is totally determined by using the Bessel function of the corresponding order.However,the Bessel function has a special characteristic which leads to the amplitude of all lower frequency components of square transform equal to zeros.In order to overcome this shortcoming,time lag quadratic transform is proposed to demodulate FM signals.The time lag can break the special characteristic of the Bessel function,so the FM signals can be demodulated by the new method.In the end,simulation and gear signals are analyzed,and the results verifies the validity of the proposed method.