Abstract: To enhance the analytical accuracy of vibration signals in a mechanical speed-change process, a non-linear relationship between the measurement systems of speed-change and the time varying statistic characteristics of the signalswas established by analyzing themeasurementprocess for a rotating machine. The Hilbert transform was applied to give the expression of instantaneous parameters of the signals. The research shows that the aberration of frequency spectra induced by the change of speed can be avoidedwhenmeasured signals are dealtwith through interpolation in light of the instantaneous frequency to gain the frequency spectra ofvibration signals.