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Construction of Symmetric Orthogonal Multiwavelets with Support [0; 2L]

Xiaoxia Feng, Zhongpeng Yang, Zhengxing Cheng

Abstract


In this paper, we propose a general method to construct symmetric multiwavelets from given symmetric multiscaling functions with support [0; 2L], and their corresponding lowpass and highpass filters have the same odd length 2L+1. Firstly, by several transforms, this problem can be reduced to the design of the filters with the length 2L starting from given filters with the length 2L. Secondly, applying the paraunitary extension of matrix and parameterizatian, we obtain the filters with these length 2L. Lastly, by the corresponding inverse transforms, the highpass filters with the length 2L + 1 can be derived. Furthermore, we design a more efficient algorithm constructing orthogonal multiwavelets with support [0; 2L]. By our algorithm, Chui-Lian multiwavelet with support [0; 2] is recovered easily.

Keywords


multiwavelet, multifilter bank, polyphase matrix, orthogonality, symmetry, parameterization.

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