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Standard pairs and construction of multiwavelets using refinement masks satisfying sum rules of order one

P. Poornima

Department of Mathematics, National Institute of Technology, Tiruchirappalli 620015, Tamil Nadu, India

E-mail Address: pnimapari@gmail.com

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and

K. Murugesan

https://orcid.org/0000-0002-6122-6455

Department of Mathematics, National Institute of Technology, Tiruchirappalli 620015, Tamil Nadu, India

E-mail Address: murugu@nitt.edu

Corresponding author.

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https://doi.org/10.1142/S0219691322500606Cited by:3 (Source: Crossref)

Abstract

A multiwavelet is typically constructed starting from a vector-valued function satisfying a matrix refinement equation. The approximation order of such a refinable function vector is related to the sum rules of order $p$ $p$ satisfied by the corresponding refinement mask. A refinable function vector can be obtained using cascade algorithm by constructing a refinement mask which satisfies the sum rules of order $1 .$ $1 .$ A standard pair associated with a refinement mask gives information about its spectral properties. In this paper, we present a procedure for constructing refinement masks satisfying the sum rules of order $1$ $1$ , starting from standard pairs. How this helps in the construction of asymmetric multiwavelets using standard pairs is illustrated through examples. A sufficient condition on a standard pair and a necessary and sufficient condition on a left standard pair are established so that the corresponding refinement mask satisfies the sum rules of order $1$ $1$ .

Keywords:

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