Unified approach for constructing multiwavelets with approximation order using refinable super-functions
Unified approach for constructing multiwavelets with approximation order using refinable super-functions
- Author(s): H. Özkaramanli
- DOI: 10.1049/ip-vis:20030497
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- Author(s): H. Özkaramanli 1
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View affiliations
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Affiliations:
1: Department of Electrical and Electronics Engineering, Eastern Mediterranean University, Magosa, Turkey
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Affiliations:
1: Department of Electrical and Electronics Engineering, Eastern Mediterranean University, Magosa, Turkey
- Source:
Volume 150, Issue 3,
June 2003,
p.
143 – 152
DOI: 10.1049/ip-vis:20030497 , Print ISSN 1350-245X, Online ISSN 1359-7108
A unified approach for constructing a large class of multiwavelets is presented. This class includes Geronimo–Hardin–Massopust, Alpert, finite element and Daubechies-like multiwavelets. The approach is based on the characterisation of approximation order of r multiscaling functions using a known compactly supported refinable super-function. The characterisation is formulated as a generalised eigenvalue equation. The generalised left eigenvectors of the finite down-sampled convolution matrix Lf give the coefficients in the finite linear combination of multiscaling functions that produce the desired super-function. The unified approach based on the super-function theory can be used to construct new multiwavelets with short support, high approximation order and symmetry.
Inspec keywords: signal sampling; function approximation; matrix algebra; eigenvalues and eigenfunctions; signal synthesis; wavelet transforms; convolution; finite element analysis
Other keywords:
Subjects: Integral transforms in numerical analysis; Signal processing and detection; Linear algebra (numerical analysis); Finite element analysis; Integral transforms in numerical analysis; Interpolation and function approximation (numerical analysis); Linear algebra (numerical analysis); Interpolation and function approximation (numerical analysis); Signal processing theory; Finite element analysis
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