Chen Jun-li, Lu En-bo, Cao Wen-jia. Sampling Theorem for Multiwavelet Subspaces[J]. Journal of Electronics & Information Technology, 2007, 29(6): 1389-1393. doi: 10.3724/SP.J.1146.2005.01320
Citation:
Chen Jun-li, Lu En-bo, Cao Wen-jia. Sampling Theorem for Multiwavelet Subspaces[J]. Journal of Electronics & Information Technology, 2007, 29(6): 1389-1393. doi: 10.3724/SP.J.1146.2005.01320
Chen Jun-li, Lu En-bo, Cao Wen-jia. Sampling Theorem for Multiwavelet Subspaces[J]. Journal of Electronics & Information Technology, 2007, 29(6): 1389-1393. doi: 10.3724/SP.J.1146.2005.01320
Citation:
Chen Jun-li, Lu En-bo, Cao Wen-jia. Sampling Theorem for Multiwavelet Subspaces[J]. Journal of Electronics & Information Technology, 2007, 29(6): 1389-1393. doi: 10.3724/SP.J.1146.2005.01320
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