Some properties of discrete wavelet maps

Abstract The discrete wavelet transform provides a new method for the analysis of vibration signals. It allows specific features of a signal to be localized in time by decomposing the signal into a family of basis functions of finite length, called wavelets. A particular property of the method is its ability to identify and isolate the fine structure of a signal. This may be the small perturbations in an otherwise smoothly varying signal which are difficult or impossible to detect by other means. That property makes the discrete wavelet transform valuable for signature analysis in vibration monitoring as well as for applications in acoustics and speech processing. This paper is about the construction of mean-square maps to display the results of wavelet analysis and about the properties of these maps.