The parameterization of 2-channel orthogonal multifilter banks with some symmetry. (English) Zbl 1145.42011
Summary: For the 2-channel orthogonal multiwavelet systems with symmetric center \(\gamma /2\), we give the parameterization of the associated multifilter banks, whether \(\gamma\) is odd or even. When \(\gamma\) is odd, we obtain the similar results to Jiang’s, for the case that \(\gamma\) is even, we transform the parameterization of the multifilter banks into the one of the case that \(\gamma\) is odd, then by the previous results and inverse transforms, we derive the corresponding results. Using the parameterization of the multifilter banks, we easily reconstruct the Chui-Lian multiwavelet systems with support [0,2] and [0,3]. Moreover, a new orthogonal multiwavelet system with symmetric center 2 is obtained, and the corresponding multiscaling function has approximation order 2.
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 94A11 | Application of orthogonal and other special functions |
| 65T60 | Numerical methods for wavelets |
Keywords:
multiscaling function; multiwavelet; multifilter bank; symmetric or antisymmetric; parameterizationReferences:
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