Constructions of Vector-Valued Filters and Vector-Valued Wavelets

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 le...

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Veröffentlicht in:Journal of Applied Mathematics 2012-01, Vol.2012 (2012), p.277-294-020
Hauptverfasser: He, Jianxun, Huang, Shouyou
Format: Artikel
Sprache:eng
Schlagworte:
Construction
Design engineering
Fourier transforms
Function space
Mathematical analysis
Multiresolution analysis
Studies
Time series
Vectors (mathematics)
Wavelet
Wavelet analysis
Wavelet transforms
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Beschreibung
Zusammenfassung: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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2012/130939