Chyzak, Frédéric, Paule, Peter, Scherzer, Otmar, Schoisswohl, Armin, Zimmermann, Burkhard (2001)
Experimental Mathematics
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Albert Cohen, Ingrid Daubechies (1993)
Revista Matemática Iberoamericana
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We build orthonormal and biorthogonal wavelet bases of L(R) with dilation matrices of determinant 2. As for the one dimensional case, our construction uses a scaling function which solves a two-scale difference equation associated to a FIR filter. Our wavelets are generated from a single compactly supported mother function. However, the regularity of these functions cannot be derived by the same approach as in the one dimensional case. We review existing techniques to evaluate the regularity...
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...
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.
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.
Lawrence Baggett (2010)
Colloquium Mathematicae
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Classical notions of wavelets and multiresolution analyses deal with the Hilbert space L²(ℝ) and the standard translation and dilation operators. Key in the study of these subjects is the low-pass filter, which is a periodic function h ∈ L²([0,1)) that satisfies the classical quadrature mirror filter equation |h(x)|²+|h(x+1/2)|² = 2. This equation is satisfied almost everywhere with respect to Lebesgue measure on the torus. Generalized multiresolution analyses and wavelets exist in abstract...
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,...
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.
A. San Antolín (2009)
Studia Mathematica
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We characterize the low pass filters associated with scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear invertible map A: ℝⁿ → ℝⁿ such that A(ℤⁿ) ⊂ ℤⁿ and all (complex) eigenvalues of A have modulus greater than 1. This characterization involves the notion of filter multiplier of such a multiresolution analysis. Moreover, the paper contains a characterization of the measurable functions...
Wim Sweldens, Ingrid Daubechies (1998)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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Bildea, Stefan, Dutkay, Dorin Ervin, Picioroaga, Gabriel (2005)
The New York Journal of Mathematics [electronic only]
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Karoui, Abderrazek (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Emil Keleveđiev, Andrey Andreev (2006)
Review of the National Center for Digitization
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