Discrete wavelet transforms over finite sets which are translation invariant L. Kamstra Probability, Networks and Algorithms (PNA)

This paper deals with the study of the spectral components of Lamb waves generated in thin aluminium plate using pulsed Nd-YAG laser and detected using a He-Ne Laser Heterodyne interferometer. Laser generation of Lamb waves leads to simultaneous generation of various frequency component as well as multiple Lamb wave modes. The Lamb wave signals are successfully and comprehensively analyzed usin...

The usefulness of wavelet analysis is demonstrated by considering analytical expressions for phase mixed Alfvén waves in different physical circumstances. The wavelet analysis is briefly introduced, using the complex-valued Morlet wavelet, consisting of a plane wave modulated by a Gaussian, as the basic wavelet. The time and scale resolution of the wavelet transform are then discussed in more d...

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete wavelet transform with real wavelets. Moreover, the hexagonal lattice allows to build wavelets having a more isotropic magnitude than on the C...

This paper presents a review on application of wavelet transform for condition monitoring and fault diagnosis of mechanical equipment. The discrete wavelet transform performs a multilevel signal decomposition to extract fault features from the vibration signal. A review on all the literature of condition monitoring using wavelet transform is certainly not possible. The purpose of this review pa...

Wavelet analysis, although used extensively in many areas of applied sciences, has not yet fully entered the economics discipline, even if many economic processes are the result of the actions of several agents who simultaneously operate at different horizons and/or have different term objectives. Wavelets provide a unique decomposition of time series observations that enable one to decompose t...

The notion of wavelets is defined. It is briefly described what are wavelets, how to use them, when we do need them, why they are preferred and where they have been applied. Then one proceeds to the multiresolution analysis and fast wavelet transform as a standard procedure for dealing with discrete wavelets. It is shown which specific features of signals (functions) can be revealed by this ana...

This talk at Fradkin conference is devoted to brief description of latest results in two topics I worked on during last years. The multiresolution analysis and fast wavelet transform became a standard procedure for pattern recognition and I describe how it has been used for analysis of high energy nucleus-nucleus interactions 1. Latest QCD results on multiplicities in quark and gluon jets are d...