Constructions of Vector-Valued Filters and Vector-Valued Wavelets

Jianxun He and Shouyou Huang

Journal of Applied Mathematics, 2012, vol. 2012, 1-18

Abstract:

Let a = ( a 1 , a 2 , … , a m ) ∈ ℂ m be an m -dimensional vector. Then, it can be identified with an m × m circulant matrix. By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002), we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix-valued functions space.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:130939

DOI: 10.1155/2012/130939

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