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用lifting方法構造具有線性相位的雙正交小波

陳佩, 

陳佩, . 用lifting方法構造具有線性相位的雙正交小波[J]. 電子與信息學報, 2002, 24(4): 486-491.
引用本文: 陳佩, . 用lifting方法構造具有線性相位的雙正交小波[J]. 電子與信息學報, 2002, 24(4): 486-491.
Chen Pei Zhang Weidong Xu Xiaoming Xu Runsheng. Lifting-scheme-constructed wavelets: orthogonality and linear-phase property[J]. Journal of Electronics & Information Technology, 2002, 24(4): 486-491.
Citation: Chen Pei Zhang Weidong Xu Xiaoming Xu Runsheng. Lifting-scheme-constructed wavelets: orthogonality and linear-phase property[J]. Journal of Electronics & Information Technology, 2002, 24(4): 486-491.

用lifting方法構造具有線性相位的雙正交小波

Lifting-scheme-constructed wavelets: orthogonality and linear-phase property

  • 摘要: Lifting作為第2代小波的構造方法,同樣能夠構造出第1代小波。與傳統(tǒng)的Daubechies方法相比,該方法簡單易懂,并且容易用格狀結構(Lattice structrue)構造出滿足特定要求的小波。該文首先根據Lawton矩陣的性質證明了幾乎所有由此方法構造出的小波滿足雙正交條件,然后考慮如何構造具有線性相位性質的雙正交小波,最后列舉幾個例子說明lifting方法。
    Abstract: Lifting scheme, which is a new approach of constructing the second-generation wavelets, can also be used to construct first-generation ones. Compared with Daubechiess construction approach, lifting scheme can easily be grasped by readers who are not well equipped with Fourier analysis. The following fact will be proved using Lawton matrix in this paper: almost all wavelets constructed using lifting scheme satisfy the biorthogonal condition. Another topic in this paper is to ensure linear-phase property of new ones. Some examples are given to demonstrate how to construct linear-phase biorthogonal wavelets.
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  • I. Daubechies, Orthogonal bases of compactly supported wavelets, Commu. Pure Appl.Math.1988, 41(7), 909-996.[2]I. Daubechies, W. Sweldens, Factoring wavelet transforms into lifting steps, J. Fourier Anal.Appl., 1998, 4(3), 247-269.[3]W. Sweldens, The lifting scheme: A construction of second generation wavelets, SIAM J.Math.Anal., 1997, 29(2), 511-546.[4]W. Sweldens, The lifting scheme: A custom-design construction of biorthogonal wavelets, Appl.Comput. Harmon. Anal., 1996, 3(2), 186-260.[5]L. Lounsbery, T. D. DeRose, J. Warren, Multiresolution surfaces of arbitrary topological type,ACM Trans. on Graphics, 1997, 16(1), 34-73.[6]W. Lawton, Tight frames of compactly supported wavelets, J. Math. Phys., 1990, 31(8), 1898-1901.[7]W. Lawton, Necessary and sufficient conditions for constructing orthonormal wavelet bases, J.Math. Phys., 1991, 32(1), 57-61.[8]A. Cohen, I. Daubechies, Biorthogonal bases of compactly supported wavelets, Commu. Pure Appl. Math. 1992, 45, 485-560.[9]T.Q. Nguyen, P. P. Vaidyanathan, Two-channel perfect-reconstruction FIR QMF structrucs which yield linear-phase analysis and synthesis filters, IEEE Trans. on ASSP, 1989, 37(5), 676-690.
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出版歷程
  • 收稿日期:  2000-06-29
  • 修回日期:  2000-11-23
  • 刊出日期:  2002-04-19

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