tailieunhanh - Báo cáo hóa học: " Research Article Construction of Orthonormal Piecewise Polynomial Scaling and Wavelet Bases on Non-Equally Spaced Knots"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Construction of Orthonormal Piecewise Polynomial Scaling and Wavelet Bases on Non-Equally Spaced Knots | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2007 Article ID 27427 13 pages doi 2007 27427 Research Article Construction of Orthonormal Piecewise Polynomial Scaling and Wavelet Bases on Non-Equally Spaced Knots Anissa Zergainoh 1 2 Najat Chihab 1 and Jean Pierre Astruc1 1 Laboratoire de Traitement et Transport de 1 Information L2TI Institut Galilee Universite Paris 13 Avenue Jean Baptiste Clement 93 430 Villetaneuse France 2 LSS CNRS Supelec Plateau deMoulon 91 192 Gif sur Yvette France Received 6 July 2006 Revised 29 November 2006 Accepted 25 January 2007 Recommended by Moon Gi Kang 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. Copyright 2007 Anissa Zergainoh et al. 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. 1. INTRODUCTION Since the last decade the development of the multiresolution theory has been extensively studied see . 1-4 . Many science and engineering fields exploit the multiresolution approach to solve their application problems.