An Adaptive Time-frequency Representation and Its Fast Implementation

so that the gray-scale graphs can be viewed more clearly. This paper presents a fast adaptive time-frequency analysis method for dealing with the signals consisting of stationary components and transients, which are encountered very often in practice. It is developed based on the short-time Fourier transform but the window bandwidth varies along frequency adaptively. The method therefore behaves more like an adaptive continuous wavelet transform. We use B-splines as the window functions, which have near optimal time-frequency localization, and derive a fast algorithm for adaptive time-frequency representation. The method is applied to the analysis of vibration signals collected from rotating machines with incipient localized defects. The results show that it performs obviously better than the short-time Fourier transform, continuous wavelet transform, and several other most studied time-frequency analysis techniques for the given task.