Title :
The application of sampling theorem of multiwavelet subspaces
Author :
Xu, Yan-xin ; Chen, Jing-ren ; Luo, Hui
Author_Institution :
Dept. of Math., Harbin Norm Univ., Harbin
Abstract :
In this paper, Walter extended the classical Shannon sampling theorem to some wavelet subspaces. We generalize the sampling theorem for multi-wavelet subspaces to multi-wavelet subspaces with a two-scaling function of Multi Resolution Analysis (MRA) based on reproducing kernel Hilbert space. Then the reconstruction function can be expressed by multi-wavelet with two scaling function of MRA using frame theorem and Zak transform. Examples are given.
Keywords :
Hilbert spaces; signal reconstruction; signal resolution; signal sampling; wavelet transforms; Shannon sampling theorem; Zak transform; frame theorem; kernel Hilbert space; multiresolution analysis; multiwavelet subspace; scaling function; signal reconstruction; Hilbert space; Kernel; Mathematics; Multiresolution analysis; Pattern analysis; Pattern recognition; Sampling methods; Signal sampling; Space technology; Wavelet analysis; Frame; Multi-wavelet subspaces; Sampling; Wavelets;
Conference_Titel :
Wavelet Analysis and Pattern Recognition, 2008. ICWAPR '08. International Conference on
Conference_Location :
Hong Kong
Print_ISBN :
978-1-4244-2238-8
Electronic_ISBN :
978-1-4244-2239-5
DOI :
10.1109/ICWAPR.2008.4635864
