复解析小波变换与振动信号包络解调分析

阐述解析小波变换用于振动信号包络解调分析的理论基础。在解析小波傅氏频谱为一实值函数的条件下，论证一个解析小波的虚部是其实部的Hilbert变换，因而简洁地推论出“Morlet组合小波、谐波小波、谐波组合小波也是一类解析小波，它们的实部和虚部构成一对Hilbert变换对”，可用于故障调制振动信号的包络解调分析；另外，还论证了“解析小波变换系数的实部与虚部构成一对Hilbert变换对”的结论。最后，以谐波组合小波为例分析滚动轴承故障振动信号。

Complex analytic wavelet transform and vibration signals envelope-demodulation analysis

Theoretical framework of the analytic wavelet transform used for vibration signals envelope-demodulation is addressed. Under the condition that the Fourier transform of an analytic wavelet is an real-valued function, it has been demonstrated that the analytic wavelet’s imaginary part is the Hilbert transform of its real part. Therefor, it has been concisely deduced that combined Morlet wavelets, Harmonic wavelets and combined Harmonic wavelets belong to the analytic wavelets. These wavelets can also be used to the envelope-demodulation analysis of mechanical faults vibration signals, in addition to usually used complex Morlet wavelets. Finally, the combined Harmonic wavelets are employed to illustrate its envelope-demodulation application for the actual vibration signals of faulty rolling-element bearings.