Constructions of Vector‐Valued Filters and Vector‐Valued Wavelets

Jianxun He and Shouyou Huang

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: Let a = (a1, a2, …, am)∈ℂm 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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https://doi.org/10.1155/2012/130939

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:130939

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