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Parameterizations of M-Band Biorthogonal Wavelets

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Wavelet Analysis and Its Applications (WAA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2251))

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Abstract

In this paper, we consider the structure of compactly supported wavelets. And we prove that any wavelet matrix (the polyphase matrix of the scaling filter and wavelet filters) can be factored as the product of fundamental biorthgonal matrices and a constant valued matrix.

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References

  1. Bi N., Dai X. and Sun Q., Construction of compactly supported M-band wavelets, Appl. Comp. Harmonic Anal. 6(1999), pp.113–131.

    Article  MATH  MathSciNet  Google Scholar 

  2. Chui C. K. and Lian J., Construction of compactly supported symmetric and antisymmetric orthogonal wavelets with scale=3, Appl. Comput. Harmonic Anal., 2(1995), pp.21–51.

    Article  MATH  MathSciNet  Google Scholar 

  3. Cohen A., Daubechies I. and Feauveau J. C., Biorthogonal basis of compactly supported Wavelets, Commun. Pure Appl. Math., 45(5)(1992), pp.485–560.

    Article  MATH  MathSciNet  Google Scholar 

  4. Daubechies I., Ten lectures on wavelets, SIAM, Philadelphia, PA, 1992.

    MATH  Google Scholar 

  5. Han B., Symmetric orthogonal scaling functions and wavelets with dilation factor 4, Adv. Compt. Math., 8(1998), pp.221–247.

    Article  MATH  Google Scholar 

  6. Heller D. N., Rank m wavelets with n vanish moments, SIAM J. Matrix Anal. 16(2)(1994), pp.502–519.

    Article  MathSciNet  Google Scholar 

  7. Heller P. N., Resnikoff H. L. and Wells R. O. Jr., Wavelet matrices and the representation of discrete functions, in Wavelet-A Tutorial in theory and applications, C. K. Chui (ed.), Academic Press, Inc.(1992), 15–50.

    Google Scholar 

  8. Ji H. and Shen Z., Compactly supported (bi)orthogonal wavelets generated by interplatory refinable functions, Adv. Comput. Math., 111999, pp.81–104.

    Google Scholar 

  9. Soman A. K., Vaidyanathan P.P. and Nguyen T.Q., Linear phase paraunitary filter banks: theory, factorization and designs, IEEE Trans. Signal Processing 41(1993), pp.3480–3496.

    Article  MATH  Google Scholar 

  10. Soardi P., Biorthogonal M-channel compactly supported wavelets, Constr. Approx., 16(2000), pp.283–311.

    Article  MathSciNet  Google Scholar 

  11. Sun Q. and Zhang Z., M-Band scaling function with filter having vanishing moments two and minimal length, J. Math. Anal. 222(1998), pp.225–243.

    Article  MATH  MathSciNet  Google Scholar 

  12. Resnikoff H. L., Tian J. and Wells R. O. Jr, An algebraic structure of orthogonal wavelet space, Appl. Comput. Harmon. Anal., 8(2000), pp. 223–248.

    Article  MathSciNet  Google Scholar 

  13. Vaidyanathan P. P., Multi-rate systems and filter banks, Prentice-Hall, Englewood Cliffs, NJ, 1993.

    Google Scholar 

  14. Vetterli M. and Herley C., Wavelet and filter banks: Theory and design, IEEE Trans. Acounst. Speech SignaL Processing, 40(1992), pp. 2207–2232.

    Article  MATH  Google Scholar 

  15. Welland G. V. and Lundberg M., Construction of compact p-wavelets, Constr. Approx. 9(1993), pp.347–370.

    Article  MATH  MathSciNet  Google Scholar 

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Authors
  1. Zeyin Zhang
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  2. Daren Huang
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Yuan Y. Tang , Pong C. Yuen  & Chun-hung Li ,  & 

  2. Department of Mathematics, Washington University, Cupples I, Campus Box 1146, 63130, St. Louis, Missouri, USA

    Victor Wickerhauser

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© 2001 Springer-Verlag Berlin Heidelberg

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Zhang, Z., Huang, D. (2001). Parameterizations of M-Band Biorthogonal Wavelets. In: Tang, Y.Y., Yuen, P.C., Li, Ch., Wickerhauser, V. (eds) Wavelet Analysis and Its Applications. WAA 2001. Lecture Notes in Computer Science, vol 2251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45333-4_55

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  • DOI: https://doi.org/10.1007/3-540-45333-4_55

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43034-6

  • Online ISBN: 978-3-540-45333-8

  • eBook Packages: Springer Book Archive

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