Displaying similar documents to “Wavelets generated by the Rudin-Shapiro polynomials”

On the exact values of coefficients of coiflets

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...

On the computation of scaling coefficients of Daubechies' 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.

Construction of Non-MSF Non-MRA Wavelets for L²(ℝ) and H²(ℝ) from MSF Wavelets

Aparna Vyas (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Considering symmetric wavelet sets consisting of four intervals, a class of non-MSF non-MRA wavelets for L²(ℝ) and dilation 2 is obtained. In addition, we obtain a family of non-MSF non-MRA H²-wavelets which includes the one given by Behera [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178].

Recent developments in wavelet methods for the solution of PDE's

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.

Application of the Haar wavelet method for solution the problems of mathematical calculus

Ü. Lepik, H. Hein (2015)

Waves, Wavelets and Fractals

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In recent times the wavelet methods have obtained a great popularity for solving differential and integral equations. From different wavelet families we consider here the Haar wavelets. Since the Haar wavelets are mathematically most simple to be compared with other wavelets, then interest to them is rapidly increasing and there is a great number of papers,where thesewavelets are used tor solving problems of calculus. An overview of such works can be found in the survey paper by Hariharan...

MRA super-wavelets.

Bildea, Stefan, Dutkay, Dorin Ervin, Picioroaga, Gabriel (2005)

The New York Journal of Mathematics [electronic only]

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Wavelets and prediction in time series

Mošová, Vratislava

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Wavelets (see [2, 3, 4]) are a recent mathematical tool that is applied in signal processing, numerical mathematics and statistics. The wavelet transform allows to follow data in the frequency as well as time domain, to compute efficiently the wavelet coefficients using fast algorithm, to separate approximations from details. Due to these properties, the wavelet transform is suitable for analyzing and forecasting in time series. In this paper, Box-Jenkins models (see [1, 5]) combined...

Non-MSF Wavelets for the Hardy Space H²(ℝ)

Biswaranjan Behera (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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All wavelets constructed so far for the Hardy space H²(ℝ) are MSF wavelets. We construct a family of H²-wavelets which are not MSF. An equivalence relation on H²-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H²-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.

Wavelet transform and binary coalescence detection

Jean-Michel Innocent, Bruno Torrésani (1997)

Banach Center Publications

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We give a short account of some time-frequency methods which are relevant in the context of gravity waves detection. We focus on the case of wavelet analysis which we believe is particularly appropriate. We show how wavelet transforms can lead to efficient algorithms for detection and parameter estimation of binary coalescence signals. In addition, we give in an appendix some of the ingredients needed for the construction of discrete wavelet decompositions and corresponding fast algorithms. ...