Wavelet transforms are attracting increasing interest in computer vision because they provide a mathematical tool for multiscale image analysis. In this paper, we show that i) the subsampled wavelet multiresolution representation is translationally variant; and ii) a wavelet transform of a signal generally confounds the phase component of the analysing wavelet associated with that scale and orientation. The importance of this observation is that commonly used features in texture analysis also depend on this phase component. This not only causes unnecessary spatial variation of features at each scale but also makes it more difficult to match features across scales.