Topic
Multiresolution analysis
About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.
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TL;DR: This work designs a cubic spline wavelet-like decomposition for the Sobolev space, and proposes a collocation method for the initial boundary value problem of nonlinear partial differential equations (PDEs) and applies it to solve linear and nonlinear PDEs.
Abstract: We have designed a cubic spline wavelet-like decomposition for the Sobolev space $H_0^2 (I)$ where I is a bounded interval. Based on a special point value vanishing property of the wavelet basis functions, a fast discrete wavelet transform (DWT) is constructed. This DWT will map discrete samples of a function to its wavelet expansion coefficients in at most $7N\log N$ operations. Using this transform, we propose a collocation method for the initial boundary value problem of nonlinear partial differential equations (PDEs). Then, we test the efficiency of the DWT and apply the collocation method to solve linear and nonlinear PDEs.
128 citations
TL;DR: The result shows that the Fourier-wavelet descriptor is an efficient representation which can provide for reliable recognition of complex patterns such as roadsigns, keys, aircrafts, characters, etc.
125 citations
TL;DR: In this paper, the authors compared three signal processing tools for power quality analysis: the continuous wavelet transform, the multiresolution analysis and the quadratic transform, and showed that the Fourier transform appears to be a reliable method for detecting and measuring voltage sags, flicker and transients.
Abstract: This paper deals with the comparison of new signal processing tools for power quality analysis. Three new signal processing techniques are considered: the continuous wavelet transform, the multiresolution analysis and the quadratic transform. Their theoretical behaviours are investigated using the basic theory of the Fourier transform. Then, examples of the four most frequent disturbances met in the power system are chosen. Finally, each kind of electrical disturbance is analyzed with example representing each tool. A qualitative comparison of results shows the advantages and drawbacks of each new signal processing technique applied to voltage disturbance analysis. The continuous wavelet transform appears to be a reliable method for detecting and measuring voltage sags, flicker and transients in power quality analysis.
125 citations
TL;DR: In this article, the authors consider the link between the Brownian motion presented by the first author in some earlier papers in the context of cosmology and the multiresolution analysis based on the wavelet transform.
Abstract: In this paper, starting from El Naschie E -infinity Cantorian space–time, we consider the link between the Brownian motion presented by the first author in some earlier papers in the context of cosmology and the multiresolution analysis based on the wavelet transform. We will consider the hypothesis that the present hierarchical segregated Universe is the effect of an expansion, which follows a scaling law. We will give a mathematical method to support El Naschie’s picture of the resolution dependence of the observations. In other words, this confirms the vision in which everything we see or measure is resolution dependent.
125 citations
TL;DR: In this paper, a wavelet decomposed ensemble model is proposed to improve the forecasting accuracy of crude oil price with deeper understanding of the market microstructure, which is based on the Heterogeneous Market Hypothesis.
124 citations