Abstract：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.
2010, Vol. 29 
