M带Walter子波抽样定理

张建康; 保铮; 焦李成

M带Walter子波抽样定理

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出版历程
- 收稿日期: 1997-09-15
- 修回日期: 1998-12-16
- 刊出日期: 1999-09-19

M-BAND WALTER WAVELET SAMPLING THEOREM

摘要

摘要: 本文把2带的Walter子波抽样定理扩展到M带子波空间,构造出一类M带紧支撑正交插值尺度函数,并在一定范围内将其参数化。举例构造并证明了一个2阶3带插值尺度函数不仅是正交的,而且也是连续的。具有这样性质的Walter抽样定理(1992)在对多分辨空间的信号进行D/A转换时,除了计算机的有限字长误差外,没有任何截断误差。
- M带正交子波; Walter子波抽样定理; 插值尺度函数
Abstract: 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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参考文献(1)

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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