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M帶Walter子波抽樣定理

張建康,  保錚,  焦李成

張建康, 保錚, 焦李成. M帶Walter子波抽樣定理[J]. 電子與信息學(xué)報(bào), 1999, 21(5): 606-612.
引用本文: 張建康, 保錚, 焦李成. M帶Walter子波抽樣定理[J]. 電子與信息學(xué)報(bào), 1999, 21(5): 606-612.
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帶Walter子波抽樣定理

M-BAND WALTER WAVELET SAMPLING THEOREM

  • 摘要: 本文把2帶的Walter子波抽樣定理擴(kuò)展到M帶子波空間,構(gòu)造出一類M帶緊支撐正交插值尺度函數(shù),并在一定范圍內(nèi)將其參數(shù)化。舉例構(gòu)造并證明了一個(gè)2階3帶插值尺度函數(shù)不僅是正交的,而且也是連續(xù)的。具有這樣性質(zhì)的Walter抽樣定理(1992)在對(duì)多分辨空間的信號(hào)進(jìn)行D/A轉(zhuǎn)換時(shí),除了計(jì)算機(jī)的有限字長(zhǎng)誤差外,沒(méi)有任何截?cái)嗾`差。
    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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  • 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]張建康,保錚,于宏毅.M帶離散小波變換中正交小波的逼近性能分析.中國(guó)科學(xué)(E輯).1997, 27(6): 556-
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出版歷程
  • 收稿日期:  1997-09-15
  • 修回日期:  1998-12-16
  • 刊出日期:  1999-09-19

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