Antoine Ayache (1999)
Revista Matemática Iberoamericana
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By means of simple computations, we construct new classes of non separable QMF's. Some of these QMF's will lead to non separable dyadic compactly supported orthonormal wavelet bases for L(R) of arbitrarily high regularity.
Dana Černá, Václav Finěk (2004)
Open Mathematics
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In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.
Dana Černá, Václav Finěk, Karel Najzar (2008)
Open Mathematics
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In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling...
Silvia Bertoluzza (2005)
Bollettino dell'Unione Matematica Italiana
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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.
Chyzak, Frédéric, Paule, Peter, Scherzer, Otmar, Schoisswohl, Armin, Zimmermann, Burkhard (2001)
Experimental Mathematics
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Aline Bonami, Sylvain Durand, Guido Weiss (1996)
Revista Matemática Iberoamericana
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One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with reasonable (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular,...
Abdolaziz Abdollahi, Jahangir Cheshmavar, Mohsen Taghavi (2011)
Open Mathematics
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In this paper, we consider the well-known Rudin-Shapiro polynomials as a class of constant multiples of low-pass filters to construct a sequence of compactly supported wavelets.
Antoine Ayaghe (2000)
Studia Mathematica
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We prove the existence of nonseparable, orthonormal, compactly supported wavelet bases for of arbitrarily high regularity by using some basic techniques of algebraic and differential geometry. We even obtain a much stronger result: “most” of the orthonormal compactly supported wavelet bases for , of any regularity, are nonseparable
Philip Gressman (2001)
Collectanea Mathematica
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In this paper the theory of wavelets on the integers is developed. For this, one needs to first find analogs of translations and dyadic dilations which appear in the classical theory. Translations in l2(Z) are defined in the obvious way, taking advantage of the additive group structure of the integers. Dyadic dilations, on the other hand, pose a greater problem. In the classical theory of wavelets on the real line, translation T and dyadic dilation T obey the commutativity relation DT^2...
Stéphane Jaffard (1991)
Publicacions Matemàtiques
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In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces C , and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet...