Open Access

Construction of Orthonormal Piecewise Polynomial Scaling and Wavelet Bases on Non-Equally Spaced Knots

EURASIP Journal on Advances in Signal Processing20072007:027427

Received: 6 July 2006

Accepted: 25 January 2007

Published: 28 March 2007


This paper investigates the mathematical framework of multiresolution analysis based on irregularly spaced knots sequence. Our presentation is based on the construction of nested nonuniform spline multiresolution spaces. From these spaces, we present the construction of orthonormal scaling and wavelet basis functions on bounded intervals. For any arbitrary degree of the spline function, we provide an explicit generalization allowing the construction of the scaling and wavelet bases on the nontraditional sequences. We show that the orthogonal decomposition is implemented using filter banks where the coefficients depend on the location of the knots on the sequence. Examples of orthonormal spline scaling and wavelet bases are provided. This approach can be used to interpolate irregularly sampled signals in an efficient way, by keeping the multiresolution approach.


Information TechnologyBasis FunctionQuantum InformationBounded IntervalFilter Bank


Authors’ Affiliations

Laboratoire de Traitement et Transport de l'Information (L2TI), Institut Galilée, Université Paris 13, Villetaneuse, France
LSS/CNRS, Supélec, Plateau de Moulon, Gif sur Yvette, France


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© Anissa Zergaïnoh et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.