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A fast algorithm for constructing orthogonal multiwavelets

Published online by Cambridge University Press:  17 February 2009

Yang Shouzhi
Yang Shouzhi
Affiliation:
Department of Mathematics, Shantou University, Shantou 515063, P.R. China; e-mail: [email protected].
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Abstract

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Multiwavelets possess some nice features that uniwavelets do not. A consequence of this is that multiwavelets provide interesting applications in signal processing as well as in other fields. As is well known, there are perfect construction formulas for the orthogonal uniwavelet. However, a good formula with a similar structure for multiwavelets does not exist. In particular, there are no effective methods for the construction of multiwavelets with a dilation factor a (a ≥ 2, a ∈ Z). In this paper, a procedure for constructing compactly supported orthonormal multiscaling functions is first given. Based on the constructed multiscaling functions, we then propose a method of constructing multiwavelets, which is similar to that for constructing uniwavelets. In addition, a fast numerical algorithm for computing multiwavelets is given. Compared with traditional approaches, the algorithm is not only faster, but also computationally more efficient. In particular, the function values of several points are obtained simultaneously by using our algorithm once. Finally, we give three examples illustrating how to use our method to construct multiwavelets.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 2 , October 2004 , pp. 185 - 200
Copyright
Copyright © Australian Mathematical Society 2004

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