Multi-wavelets from B-spline super-functions with approximation order
Data(s) |
01/08/2002
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Resumo |
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 <b>H</b> 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 <b>H<i><sub>f</sub></i></b>; a finite portion of <b>H</b> 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.<br /> |
Identificador | |
Idioma(s) |
eng |
Publicador |
Elsevier BV |
Relação |
http://dx.doi.org/10.1016/S0165-1684(02)00212-8 |
Direitos |
2002, Elsevier Science B.V |
Palavras-Chave | #Multi-wavelets #Scalar wavelets #Orthogonality #Approximation order #Symmetry #Superfunction #B-spline |
Tipo |
Journal Article |