Constructions of Vector-Valued Filters and Vector-Valued Wavelets
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/130939 |
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| author | Jianxun He Shouyou Huang |
| author_facet | Jianxun He Shouyou Huang |
| author_sort | Jianxun He |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-79a7637eb38b470c87be249df266a0a1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-79a7637eb38b470c87be249df266a0a12025-08-20T03:35:47ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/130939130939Constructions of Vector-Valued Filters and Vector-Valued WaveletsJianxun He0Shouyou Huang1School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, ChinaLet 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.http://dx.doi.org/10.1155/2012/130939 |
| spellingShingle | Jianxun He Shouyou Huang Constructions of Vector-Valued Filters and Vector-Valued Wavelets Journal of Applied Mathematics |
| title | Constructions of Vector-Valued Filters and Vector-Valued Wavelets |
| title_full | Constructions of Vector-Valued Filters and Vector-Valued Wavelets |
| title_fullStr | Constructions of Vector-Valued Filters and Vector-Valued Wavelets |
| title_full_unstemmed | Constructions of Vector-Valued Filters and Vector-Valued Wavelets |
| title_short | Constructions of Vector-Valued Filters and Vector-Valued Wavelets |
| title_sort | constructions of vector valued filters and vector valued wavelets |
| url | http://dx.doi.org/10.1155/2012/130939 |
| work_keys_str_mv | AT jianxunhe constructionsofvectorvaluedfiltersandvectorvaluedwavelets AT shouyouhuang constructionsofvectorvaluedfiltersandvectorvaluedwavelets |