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Fractals Based on Harmonic Wavelets

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Book cover Computational Science and Its Applications – ICCSA 2009 (ICCSA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5592))

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Abstract

In this paper a simple algorithm based on harmonic wavelets is given for the generation of self similar functions. Due to their self similarity property and scale dependence, harmonic wavelets might offer a good approximation of fractals by a very few instances of the wavelet series and a more direct interpretation of the scale invariance for deterministic localized fractals.

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References

  1. Abry, P., Goncalves, P., Lévy-Véhel, J.: Lois d’éschelle, Fractales et ondelettes, Hermes (2002)

    Google Scholar 

  2. Arnéodo, A., Grasseau, G., Holschneider, M.: Wavelet Transform of Multifractals. Phys. Review Letters 61(20), 2281–2284 (1988)

    Article  MathSciNet  Google Scholar 

  3. Borgnat, P., Flandrin, P.: On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation. Applied and Computational Harmonic Analysis 15, 134–146 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cattani, C.: Harmonic Wavelets towards Solution of Nonlinear PDE. Computers and Mathematics with Applications 50(8-9), 1191–1210 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cattani, C., Rushchitsky, J.J.: Wavelet and Wave Analysis as applied to Materials with Micro or Nanostructure. Series on Advances in Mathematics for Applied Sciences, p. 74. World Scientific, Singapore (2007)

    Book  MATH  Google Scholar 

  6. Cattani, C.: Wavelet extraction of a pulse from a periodic signal. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds.) ICCSA 2008, Part I. LNCS, vol. 5072, pp. 1202–1211. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Cattani, C.: Shannon Wavelets Theory. Mathematical Problems in Engineering 2008, pgs. 24 (2008); Article ID 164808

    Google Scholar 

  8. Cattani, C.: Harmonic Wavelet Approximation of Random, Fractal and High Frequency Signals. Telecommunication Systems (to appear, 2009)

    Google Scholar 

  9. Chui, C.K.: An Introduction to Wavelets. Academic Press, New York (1992)

    MATH  Google Scholar 

  10. Daubechies, I.: Ten Lectures on wavelets. SIAM, Philadelphia (1992)

    Book  MATH  Google Scholar 

  11. Dutkay, D.E., Jorgensen, P.E.T.: Wavelets on Fractals. Rev. Mat. Iberoamericana 22(1), 131–180 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Falconer, K.: Fractal Geometry. John Wiley, New York (1977)

    MATH  Google Scholar 

  13. Jorgensen, P.E.T.: Analysis and Probability, Wavelets, Signals, Fractals. Graduate Texts in Mathematics, vol. 234. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  14. Mallat, S.: A Wavelet tour of signal processing. Academic Press, London (1998)

    MATH  Google Scholar 

  15. Muniandy, S.V., Moroz, I.M.: Galerkin modelling of the Burgers equation using harmonic wavelets. Phys. Lett. A 235, 352–356 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Newland, D.E.: Harmonic wavelet analysis. Proc. R. Soc. Lond. A 443, 203–222 (1993)

    Article  MATH  Google Scholar 

  17. Wornell, G.: Signal Processing with Fractals: A Wavelet-Based Approach. Prentice-Hall, Englewood Cliffs (1996)

    Google Scholar 

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Author information

Authors and Affiliations

  1. DiFarma, University of Salerno, Via Ponte Don Melillo, I-84084, Fisciano (SA), Italy

    Carlo Cattani

Authors
  1. Carlo Cattani
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

  2. School of Business Systems, Monash University, 3800, Clayton, Victoria, Australia

    David Taniar

  3. L.I.S.U.T. - D.A.P.I.T., University of Basilicata, Viale dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Beniamino Murgante

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, 06123, Perugia, Italy

    Antonio Laganà

  5. School of Computing, Computer Communication Laboratory, SoongSil University, 1-1 Sang-do 5 Dong, Dong-jak Ku, 156-743, Seoul, Korea

    Youngsong Mun

  6. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

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© 2009 Springer-Verlag Berlin Heidelberg

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Cattani, C. (2009). Fractals Based on Harmonic Wavelets. In: Gervasi, O., Taniar, D., Murgante, B., Laganà, A., Mun, Y., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2009. ICCSA 2009. Lecture Notes in Computer Science, vol 5592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02454-2_56

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  • DOI: https://doi.org/10.1007/978-3-642-02454-2_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02453-5

  • Online ISBN: 978-3-642-02454-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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