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Volume 24 Issue 4
Apr.  2002
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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.

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

  • Received Date: 2000-06-29
  • Rev Recd Date: 2000-11-23
  • Publish Date: 2002-04-19
  • 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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