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Short wavelets and matrix dilation equations

IEEE Transactions on Signal Processing, 1995
Scaling functions and orthogonal wavelets are created from the coefficients of a lowpass and highpass filter (in a two-band orthogonal filter bank). For "multifilters" those coefficients are matrices. This gives a new block structure for the filter bank, and leads to multiple scaling functions and wavelets.
G. Strang, V. Strela
semanticscholar   +2 more sources

Wavelets and Dilation Equations: A Brief Introduction

SIAM Review, 1989
Wavelets are new families of basis functions that yield the representation $f(x) = \sum {b_{jk} W(2^j x - k)} $. Their construction begins with the solution $\phi (x)$ to a dilation equation with coefficients $c_k $. Then W comes from $\phi $, and the basis comes by translation and dilation of W.
G. Strang
semanticscholar   +2 more sources

Functional-Differential Equations with Dilation and Symmetry

Siberian Mathematical Journal, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L. E. Rossovskii, A. A. Tovsultanov
openaire   +1 more source

Wavelets and differential-dilation equations

IEEE Transactions on Signal Processing, 1996
Summary: It is shown how differential-dilation equations can be constructed using iterations, similar to the iterations with which wavelets and dilation equations are constructed. A continuous-time wavelet is constructed starting from a differential-dilation equation.
Cooklev, Todor   +2 more
openaire   +2 more sources

Energy equation and stress–dilatancy relationship for sand

Acta Geotechnica, 2021
The energy equation is an expression of the first law of thermodynamics or the law of conservation of energy. According to the first law of thermodynamics, the externally applied work to a system is equal to the sum of dissipation energy and Helmholtz free energy of the system. However, most of the currently available stress–dilatancy relationships are
Ching S. Chang, Yibing Deng
openaire   +1 more source

Sensitivity analysis of shock wave Burgers’ equation via a novel algorithm based on scale-3 Haar wavelets

International Journal of Computational Mathematics, 2017
In this paper, a novel technique is being formulated for the numerical solutions of Shock wave Burgers' equations for planar and non-planar geometry. It is well known that Burgers' equation is sensitive to the perturbations in the diffusion term. Thus we
R. C. Mittal, Sapna Pandit
semanticscholar   +1 more source

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