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Volume 21 Issue 5
Sep.  1999
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Zhang Jiankang, Bao Zheng, Jiao Licheng. M-BAND WALTER WAVELET SAMPLING THEOREM[J]. Journal of Electronics & Information Technology, 1999, 21(5): 606-612.
Citation: Zhang Jiankang, Bao Zheng, Jiao Licheng. M-BAND WALTER WAVELET SAMPLING THEOREM[J]. Journal of Electronics & Information Technology, 1999, 21(5): 606-612.

M-BAND WALTER WAVELET SAMPLING THEOREM

  • Received Date: 1997-09-15
  • Rev Recd Date: 1998-12-16
  • Publish Date: 1999-09-19
  • This paper constructs a family of M-band orthogonal compactly supported interpolating scaling function, gives a 3-band scaling function and shows that it is not only compactly supported, but also orthogonal and continuous. G.Walter s wavelet sampling theorem(1992) corresponding to the scaling function has the compactly supported interplant. Therefore, the signals in multiresolution subspaces can be reconstructed exactly and quickly without any truncated errors except finite field length errors.
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  • Walter G G. A sampling theorem for wavelet subspaces, IEEE Trans. on IT, 1992, IT-38(2): 881-884.[2]Aldroubi A, Unser M. Families of wavelet transforms in connection with Shannon's sampling theorem and the Gabor transform. Wavelets: A Tutorial in Theory and Applications,C.K.Chui, Ed. New York: Academic, 1992, 509-528.[3]Janssen A J E M. The Zak transform and sampling theorems for wavelet subspaces[J].IEEE Trans. Signal Processing.1993, 41(12):3360-3524[4]Xia X G, Zhang Z. On sampling theorem, wavelets, and wavelet transforms[J].IEEE Trans. Signal Processing.1993, 41(12):3524-3535[5]Djokovic I, Vaidyanathan P P. New sampling theorems for MAR subspaces. Proc. ICASSP 1995, 1085-1088.[6]Sweldens W, Piessens R. Wavelet sampling techniques. Proceeding of Joint Statistical Meetings, San Francisco: August 1993, 20-29.[7]Shena M J. The discrete Wavelet transform: Wedding the Atrous and Mallat algorithm. IEEE Trans. on SP. 1992, SP-40(10): 2464-2482.[8]Sweldens W. The lifting scheme: A custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal. 1996, 3(2): 186-200.[9]Lawton W M. Necessary and sufficient conditions for constructing orthonormal waveletw bases. J. Math. Physics. 1991, 32(1): 57-61.[10]Steffen P, Heller P, Gopinath R A, Burrus C S. Theory of regular M-band wavelet bases IEEE Trans. on SP. 1993, SP-41(12): 3497-3510.[11]Sweldens W, Piessens R. Asymptotic error expansions for wavelet approximations of smooth functions II. Numer. Math. 1994, 68(3): 377-401.[12]Unser M. Approximation power of biorthogonal wavelet expansions. IEEE Trans. on SP, 1996, SP-44(3): 519-527.[13]张建康,保铮,于宏毅.M带离散小波变换中正交小波的逼近性能分析.中国科学(E辑).1997, 27(6): 556-
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