A new analysis method using wavelet domain for steady-state operating condition of power system is developed and introduced. Based on wavelet-Galerkin theory, the system components such as resistor, inductor, capacitor, transmission lines, and switching devices are modeled in discrete wavelet domain for the purpose of steady-state analysis. To solve system equations, they are transferred to wav...

I would like to congratulate Professor Antoniadis for successfully outlining the current state-of-art of wavelet applications in statistics. Since wavelet techniques were introduced to statistics in the early 90's, the applications of wavelet techniques have mushroomed. There is a vast forest of wavelet theory and techniques in statistics and one can find himself easily lost in the jungle. The ...

In this paper we present an overview of how geometric methods can be successfully used to solve problems in Analysis. We will focus on selfsimilar objects and use their structure to construct frames, Riesz bases and wavelet bases in R with a single generator function. Further, we show that the generating functions for these systems are dense in L2(R).

In this note it is only possible to give a short description of affine wavelet theory and to indicate some reasons, why wavelet theory has attracted so much attention from the applied community recently. Besides a description of the basic ideas this note provides a guide to the relevant literature (published or presently submitted for publication) and some recent developments which are of inter...

A wavelet is a basis function used to construct a wavelet transform. The first known wavelet – Haar wavelet was proposed in 1909 by Alfred Haar. Wavelet theory has been applied to various problems including signal processing in communications, image compression-extraction, solution of the linear and nonlinear integral equations etc. Haar wavelet based discretization technique is adopted for sol...

As a novel data mining approach, a wavelet entropy algorithm is used to perform entropy statistics on wavelet coefficients (or reconstructed signals) at various wavelet scales on the basis of wavelet decomposition and entropy statistic theory. Shannon wavelet energy entropy, one kind of wavelet entropy algorithm, has been taken into consideration and utilized in many areas since it came into be...

1. introduction in recent years, regarding climate changes, the analysis of natural variability of climate at different time scales has attracted a lot of attention. while, the data series with short statistical period just shows a likelihood estimation of a few decades of climate variability, the data series with long period shows the fluctuations of several decades with statistical importance...

This article obtains the nonseparable version of wavelet packets on ~a and generalizes the "'unstability" result of nonorthogonal wavelet packets in Cohen-Daubechies to higher dimensional cases. 1 . I n t r o d u c t i o n The wavelet packets introduced by R. Coifman, Y. Meyer, and M. V. Wickerhauser played an important role in the applications of wavelet analysis as shown, for example, in [CMW...

With the development of the theory of wavelet transform, biorthogonal wavelet filter banks with linear phase and compact support characteristics are widely used in signal and image processing. We study the multiscale edge detection using anti-symmetrical biorthogonal wavelet filter banks with the same even length based on the analysis of the properties of this wavelet filter banks. The steps of...

With wavelet technology used more widely in deformation analysis, the paper will talk multi-wavelet (the second generation wavelet) theory used for deformation monitoring data analysis. The paper studies signal adopting different preprocessing method, makes a study of the selection problem in optima multi-wavelet preprocessing method. The deformation monitoring signal is disposed using differen...