Trigonometric interpolation and wavelet decompositions

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1995 English Publisher:Springer Science and Business Media LLCJournal:Numerical Algorithms, volume 9, pages 293-317 (issn: 1017-1398, eissn: 1572-9265,

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Authors: Jürgen Prestin; Ewald Quak;

doi: 10.1007/bf02141593

Trigonometric interpolation and wavelet decompositions

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Abstract

The problem of explicit decomposition and reconstruction algorithms for nested spaces of trigonometric polynomials is studied. The pioneering result connecting multiresolution analysis to nested spaces of trigonometric polynomials is due to \textit{C. K. Chui} and \textit{H. N. Mhaskar} [Constructive Approximation 9, No. 2-3, 167-190 (1993; Zbl 0780.42020)]. The authors first present relevant results on orthogonal trigonometric polynomial bases due to \textit{A. A. Privalov} [Mat. Sb. 182, No. 3, 384-394 (1991; Zbl 0758.42003)] in the framework of a trigonometric multiresolution analysis. Scaling functions and wavelets are given explicitly as trigonometric interpolants and decomposition and reconstruction algorithms can be described in simple matrix notation.

Related Organizations

The University of Texas System
United States
University of Rostock
Germany
Texas A&M University
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Keywords

wavelet decompositions, trigonometric interpolation, reconstruction algorithms, Numerical methods for wavelets, scaling functions, trigonometric polynomials, Nontrigonometric harmonic analysis involving wavelets and other special systems, nested spaces, multiresolution analysis

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