Construction of wavelets and multiwavelets basis : a generalized method

Bhatti, Asim 2010, Construction of wavelets and multiwavelets basis : a generalized method, LAP Lambert Academic Publishing, [Germany].

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Title Construction of wavelets and multiwavelets basis : a generalized method
Author(s) Bhatti, AsimORCID iD for Bhatti, Asim
Publication date 2010
Total pages 108 p.
Publisher LAP Lambert Academic Publishing
Place of Publication [Germany]
Keyword(s) electronics
communications technology
Summary Multiwavelets are wavelets with multiplicity r, that is r scaling functions and r wavelets, which define multiresolution analysis similar to scalar wavelets. They are advantageous over scalar wavelets since they simultaneously posse symmetry and orthogonality. In this work, a new method for constructing multiwavelets with any approximation order is presented. The method involves the derivation of a matrix equation for the desired approximation order. The condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors give the combinations of scaling functions required to reconstruct the desired spline or super function. The method is demonstrated by constructing a specific class of symmetric and non-symmetric multiwavelets with different approximation orders, which include Geranimo-Hardin-Massopust (GHM), Daubechies and Alperts like multi-wavelets, as parameterized solutions. All multi-wavelets constructed in this work, posses the good properties of orthogonality, approximation order and short support.
ISBN 9783838348322
Language eng
Field of Research 099999 Engineering not elsewhere classified
Socio Economic Objective 970109 Expanding Knowledge in Engineering
HERDC Research category A2.1 Authored - other
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Document type: Book
Collection: Centre for Intelligent Systems Research
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