Vibration signals are considered as nonstationary signals with transients. Conventional harmonic Fourier analysis finds it difficult to model the vibration signals. In this paper, a novel approach for vibration analysis and modelling is presented. This approach uses both global Fourier transforms and local wavelet analysis techniques. Time-frequency wavelet analysis is a proven tool for the detection of vibration transients. However, current algorithms with discrete or continuous wavelet transforms for vibration analysis either have low resolution of features or are very time consuming. To overcome these restrictions an autocorrelation wavelet algorithm is developed using a Gaussian wavelet filter with very narrow pass-band. Using time-frequency maps with high frequency resolution enables us to observe the evolution in time of significant frequencies identified by global Fourier analysis, so that the transients and the regular signals can be distinguished. These regular significant frequencies are selected to form the basis of our vibration model, with the coefficients of the model being identified by a least-squares algorithm, which ensures that the error is minimised. To demonstrate its usefulness for condition monitoring, the modelling technique is applied to a vibration signal recorded from a bearing application and from a machine tool spindle, and the results are reported.