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Integration of Multivariate Haar Wavelet Series
2001This article considers the error of integrating multivariate Haar wavelet series by quasi-Monte Carlo rules using scrambled digital nets. Both the worst-case and random-case errors are analyzed. It is shown that scrambled net quadrature has optimal order. Moreover, there is a simple formula for the worst-case error.
Stefan Heinrich +2 more
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1999
This chapter explains the nature of the simplest wavelets and an algorithm to compute a fast wavelet transform. Such wavelets have been called “Haar’s wavelets” since Haar’s publication in 1910 (reference [19] in the bibliography). To analyze and synthesize a signal—which can be any array of data—in terms of simple wavelets, this chapter employs shifts
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This chapter explains the nature of the simplest wavelets and an algorithm to compute a fast wavelet transform. Such wavelets have been called “Haar’s wavelets” since Haar’s publication in 1910 (reference [19] in the bibliography). To analyze and synthesize a signal—which can be any array of data—in terms of simple wavelets, this chapter employs shifts
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Haar Wavelets is a Clifford Algebra
AIP Conference Proceedings, 2007The main idea is to construct a basis for the space L2([0,1]) that can be wrapped isomorphically onto a Clifford algebra Rm of dimension 2m (m going to infinity). The endomorphism algebra End(Rm), itself a Clifford algebra, is then used to encode bounded linear operators on L2([0,1]) such as the Haar wavelet transform.
F. Sommen +3 more
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1998
The Haar basis is known since 1910. Here we consider the Haar basis on the real line IR and describe some of its properties which are useful for the construction of general wavelet systems. Let L2 (IR) be the space of all complex valued functions f on IR such that their L2-norm is finite: $$ \left\| {f\left\| {2 = \left( {\int_{ - \infty }^\infty {\
Wolfgang Härdle +3 more
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The Haar basis is known since 1910. Here we consider the Haar basis on the real line IR and describe some of its properties which are useful for the construction of general wavelet systems. Let L2 (IR) be the space of all complex valued functions f on IR such that their L2-norm is finite: $$ \left\| {f\left\| {2 = \left( {\int_{ - \infty }^\infty {\
Wolfgang Härdle +3 more
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Optical Haar wavelet transform
Optical Engineering, 1992An optical Haar mother wavelet is created with a Semetex 128 x 128 magneto-optic spatial light modulator. Two techniques for dilating the mother wavelet are explored: (1) aperture stopping and (2) operating the SLM in ternary phase-amplitude mode. Discrete resolution levels of a continuous wavelet transform are obtained by optically correlating a ...
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Generalized Haar wavelets and frames
SPIE Proceedings, 2000Generalized Haar wavelets were introduced in connection with the problem of detecting specific periodic components in noisy signals. We showed that the non-normalized continuous wavelet transform of a periodic function taken with respect to a generalized Haar wavelet is periodic in time as well as in scale, and that generalized Haar wavelets are the ...
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Fast Coding of Haar Wavelet Trees
2022 Data Compression Conference (DCC), 2022Dylan Tarter, Brian Nutter
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A numerical algorithm based on scale-3 Haar wavelets for fractional advection dispersion equation
Engineering Computations, 2021Dr. Sapna Pandit, R C Mittal
exaly