File(s) not publicly available

Multi-wavelets from B-spline super-functions with approximation order

journal contribution
posted on 2002-08-01, 00:00 authored by H Ozkaramanli, Asim BhattiAsim Bhatti, B Bilgehan
Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p−1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix Hf; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.

History

Journal

Signal processing

Volume

82

Issue

8

Pagination

1029 - 1046

Publisher

Elsevier BV

Location

Amsterdam, Netherlands

ISSN

0165-1684

eISSN

1872-7557

Language

eng

Publication classification

C1.1 Refereed article in a scholarly journal

Copyright notice

2002, Elsevier Science B.V