The characters of multiple dual pseudoframes with multiple refinable functions and a generalized multiresolution structure

Author

Sheng Zongsheng ; Li Xianghai

Author_Institution

Dept. of Appl. Math., Nanyang Inst. of Technol., Nanyang, China

Volume

1

fYear

2010

fDate

17-18 July 2010

Firstpage

202

Lastpage

205

Abstract

The notion of a generalized multiresolution structure (GMS) of L²(R) is formulated. The definition of multiple pseudoframes for subspaces of L²(R) is presented. The construction of a GMS of Paley-Wiener subspaces of L²(R) is investigated. The sufficient condition for the existence of multiple pseudoframes for subspaces of L²(R) is obtained based on such a GMS. A necessary and sufficient condition on the existence of biorthogonal multiple vector-valued wavelets is presented by means of paraunitary vector filter bank theory.

Keywords

affine transforms; channel bank filters; signal resolution; time-frequency analysis; wavelet transforms; GMS; L²(R) subspace; Paley Wiener subspace; biorthogonal multiple vector value wavelet; generalized multiresolution structure; multiple dual pseudoframe; multiple refinable function; paraunitary vector filter bank theory; time frequency analysis method; Construction industry; Fourier series; Fourier transforms; Image resolution; Multiresolution analysis; Signal resolution; Sufficient conditions; affine fames; filter functions; multiple dual pseudofames; refinable functions; time-frequency analysis method;

fLanguage

English

Publisher

ieee

Conference_Titel

Environmental Science and Information Application Technology (ESIAT), 2010 International Conference on

Conference_Location

Wuhan

Print_ISBN

978-1-4244-7387-8

Type

conf

DOI

10.1109/ESIAT.2010.5568576

Filename

5568576