We extend Robertson’s theorem to apply to frames generated by the action of a discrete, countable abelian unitary group. Within this setup we use Stone’s theorem and the theory of spectral multiplicity to analyze wandering frame collections. Motivated by wavelet theory, we explicitly apply our results to the action of the integers given by translations on L(R). This yields a new functional anal...

In this work, we present a model theory based fusion methodology for multisensor wavelet-features based recognition called Automatic Multisensor Feature-based Recognition System (AMFRS). The goal of this system is to increase accuracy of the commonly used wavelet-based recognition techniques by incorporating symbolic knowledge (symbolic features) about the domain and by utilizing a model theory...

This paper presents a generalization of the continuous wavelet transform to higher dimensions. This generalization includes previous higher dimensional generalizations as special cases, without the loss of the elegance of the one-dimensional equations. One noteworthy special case is a transform that is closely related to the cortex transform developed by Watson. This special case rmly relates t...

We construct oblique multi-wavelets bases which encompass the orthogonal multi-wavelets and the biorthogonal uni-wavelets of Cohen, Deaubechies and Feauveau. These oblique multi-wavelets preserve the advantages of orthogonal and biorthogonal wavelets and enhance the flexibility of wavelet theory to accommodate a wider variety of wavelet shapes and properties. Moreover, oblique multi-wavelets ca...

Based on a mathematical model involving Radon measure explicit computations on convolution integrals defining continuous (integral) wavelet transformations are carried out. The study shows that the truncated Morlet wavelet significantly depends on a rotation parameter and thus lay a foundation of edge detection in pattern recognition and image processing using rotational (directional) wavelets....

Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from noncommutative harmonic analysis, ergodic theory, and dynamical systems. Our analysis is in the setting of semidirect products, discrete subgroups, and solenoids. Our applications include analysis an...

This article develops a wavelet decomposition of a stochastic process which parallels a time{localized Cram er (Fourier) spectral representation. We provide a time{scale instead of a time{frequency decomposition and, hence, instead of thinking as scale in terms of \inverse frequency" we start from genuine time{scale building blocks or \atoms". Using this class of locally stationary wavelet (LSW...

The paper extends our pervious work on solving multi-contingency transient stability constrained optimal power flow problems (MC-TSCOPF) with the approach of particles swarm optimization (PSO). A hybrid PSO method that incorporates with a new wavelet theory based mutation operation, intends to improve the searching strategies on previously used PSO methods, is proposed to solve MC-TSCOPF proble...

Transformer differential protection may be of malfunction at the emergence of inrush current, and it will affect the normal operation of the transformer. So the paper puts forward a new application of wavelet energy spectrum entropy-neural network theory in transformer microcomputer protection, in which the multi-resolution analysis of wavelet transform and information entropy technology are co...

In allusion to the shortcomings of the existing signal analysis method for highfrequency analysis, non-stationary signal analysis and so on, wavelet analysis and grey theory are introduced into the signal analysis, a new signal analysis method based wavelet analysis and grey theory is proposed in this paper. In this method, the wavelet packet is used to nonredundantly, lossless and orthogonally...