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Axioms 2013, 2(2), 122-141; doi:10.3390/axioms2020122
Article

Construction of Multiwavelets on an Interval

1
 and 2,*
Received: 5 February 2013; in revised form: 21 March 2013 / Accepted: 26 March 2013 / Published: 17 April 2013
(This article belongs to the Special Issue Wavelets and Applications)
Download PDF [260 KB, uploaded 17 April 2013]
Abstract: Boundary functions for wavelets on a finite interval are often constructed as linear combinations of boundary-crossing scaling functions. An alternative approach is based on linear algebra techniques for truncating the infinite matrix of the DiscreteWavelet Transform to a finite one. In this article we show how an algorithm of Madych for scalar wavelets can be generalized to multiwavelets, given an extra assumption. We then develop a new algorithm that does not require this additional condition. Finally, we apply results from a previous paper to resolve the non-uniqueness of the algorithm by imposing regularity conditions (including approximation orders) on the boundary functions.
Keywords: wavelets on an interval; multiwavelets; discrete wavelet transform; boundary handling wavelets on an interval; multiwavelets; discrete wavelet transform; boundary handling
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Altürk, A.; Keinert, F. Construction of Multiwavelets on an Interval. Axioms 2013, 2, 122-141.

AMA Style

Altürk A, Keinert F. Construction of Multiwavelets on an Interval. Axioms. 2013; 2(2):122-141.

Chicago/Turabian Style

Altürk, Ahmet; Keinert, Fritz. 2013. "Construction of Multiwavelets on an Interval." Axioms 2, no. 2: 122-141.


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