多小波子空间采样定理
doi: 10.3724/SP.J.1146.2005.01320
Sampling Theorem for Multiwavelet Subspaces
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摘要: 该文基于再生核Hilbert空间理论，把小波子空间的Walter采样定理推广到多小波子空间，建立了多小波子空间的均匀采样定理，利用Zak变换给出了由尺度函数构造重构函数的公式。进一步针对采样点不均匀的情况，建立了多小波子空间的不规则采样定理。最后给出数值算例。
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关键词:
- 再生核;多小波;多小波子空间;采样定理
Abstract: In this paper, the multiwavelet sampling theorem from Walters wavelet sampling theorem by reproducing kernel is generalized. The reconstruction function can be expressed by multiwavelet using Zak transform. Then the general case of the irregular sampling is considered and the irregular sampling theorem for multiwavelet subspaces is established. Finally, the corresponding examples are given. -
Walter G G. A sampling theorem for wavelet subspaces[J].IEEE Trans. on IT.1992, 38(2):881-884[2]Xia X G and Zhang Z. On sampling theorem, wavelets and wavelet transforms[J].IEEE Trans. on Signal Processing.1993, 41(12):3524-3535[3]Blu T and Unser M. Approximation error for quasi- interpolators and (multi)wavelet expansions[J].Applied and Computation Harmonic Analysis.1999, 6:219-251[4]Selesnick I W. Interpolating multiwavelets bases and the sampling the orem[J].IEEE Trans. on Signal Processing.1999, 47(6):1615-1621[5]Sun W S and Zhou X W. Sampling theorem for multiwavelet subspaces[J].Chinese Science Bulletin.1999, 44(14):1283-1286[6]Jia C Y and Gao X P. A general sampling theorem for multiwavelet subspaces. Science in China(Series F), 2002, 45(5): 365-372.[7]Scholkopf B, Mika S, and Burges C J C, et al.. Input space vs. feature space in kernel-based methods. IEEE Trans. on Neural Networks, 1999, 10(5): 1000-1017.[8]Plonka G and Strela V. Construction of multi-scaling functions with approximation and symmetry[J].SIAM J. Math. Anal.1998, 29(2):1-31[9]Chui C K and Lian J. A study of orthonornal multi-wavelets[J].Appl. Numer. Math.1996, 20(3):273-298 -
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