Abstract
As a multi-resolution signal decomposition and analysis technique, the wavelet transforms have been already introduced to vibration signal processing. In this paper, a comparison on the time-scale map analysis is made between the discrete and the continuous wavelet transform. The orthogonal wavelet transform decomposes the vibration signal onto a series of orthogonal wavelet functions and the number of wavelets on one wavelet level is different from those on the other levels. Since the grids are unevenly distributed on the time-scale map, it is shown that a representation pattern of a vibration component on the map may be significantly altered or even be broken down into pieces when the signal has a shift along the time axis. On contrary, there is no such uneven distribution of grids on the continuous wavelet time-scale map, so that the representation pattern of a vibration signal component will not change its shape when the signal component shifts along the time axis. Therefore, the patterns in the continuous wavelet time-scale map are more easily recognised by human visual inspection or computerised automatic diagnosis systems. Using a Gaussian enveloped oscillation wavelet, the wavelet transform is capable of retaining the frequency meaning used in the spectral analysis, while making the interpretation of patterns on the time-scale maps easier.
Copy-Move Forgery Detection using Orthogonal Wavelet Transforms
