An algorithm for constructing symmetric orthogonal multiwavelets by matrix symmetric extension. (English) Zbl 1042.42030
Let \(\varphi _{1},\dots ,\varphi _{r}\) be functions in \(L^{2}({\mathbb R} ) \) with compact support such that the system of integer translations is orthogonal. Suppose that \(\Phi =(\varphi _{1},\dots ,\varphi _{r}) ^{t}\) is a solution of the vector refinement equation
\[
\Phi (x) =m\sum_{k\in {\mathbb Z}}h(k) \Phi (mx-k)
\]
where \(m>1\) is a fixed even number. In the paper it is assumed that the low pass filter \(H(z) \) is of the form \(H(z) =\sum_{k=0}^{(\alpha +1) m-1}h(k) z^{-k}.\) Based on the work of Q. Jiang [Adv. Comput. Math. 12, No. 2–3, 189–211 (2000; Zbl 0937.42018)] the authors show the existence of symmetric or antisymmetric multiwavelets.
Reviewer: Hermann Render (Logrono)
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 65T60 | Numerical methods for wavelets |
Citations:
Zbl 0937.42018References:
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