Discrete Wavelet Analysis

  • Ton J. Cleophas
  • Aeilko H. Zwinderman
Chapter

Abstract

Wavelets are oscillations, supposedly resulting from multiple smaller wavelets, and they are, traditionally, analyzed with polynomial, sine and cosine, and other functions. Ingrid Daubechies (1988) demonstrated that the repeated use of sharply spiked functions with multiple scales as basis functions for wavelet analysis provided better data-fit, and called it discrete wavelet analysis.

Keywords

Discrete Wavelet Wavelet Power Spectrum Sharp Spike Wavelet Calculator Energy Consumption Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Wavelet (2013) http://en.wikipedia.org/wiki/wavelet. 2 Jan 2013
  2. 2.
    Graps A (1995) An introduction to wavelets. IEEE Comput Sci Eng 2:1–16CrossRefGoogle Scholar
  3. 3.
    Merry R (2005) Wavelet theory and applications. A literature study. Eindhoven University of Technology, EindhovenGoogle Scholar
  4. 4.
    Addison PS (2005) Wavelet transforms and the ECG: a review. Physiol Meas 26:155–199CrossRefGoogle Scholar
  5. 5.
    Fourier J (1822) Theorie analytique de la chaleur. Paris, Edit. by Firmin DidotGoogle Scholar
  6. 6.
    Anonymous (1997) Haar transform. Stanford Exploration Project. University of Stanford, USA, 11-07Google Scholar
  7. 7.
    Daubechies I (1992) Ten lectures on wavelets. Society for Industrial and Applied Mathematics, ISBN 0-89871-274-2Google Scholar
  8. 8.
    Anonymous (2013). Morlet wavelet. http://en.wikipedia.org/wiki/wavelet. 2 Jan 2013
  9. 9.
    Beylkin G, Coifman R, Rokhlin V (1991) Fast wavelet transforms and numerical algorithms. Comm Pure Appl Math 44:141–183CrossRefGoogle Scholar
  10. 10.
    S-plus statistical software (2013) www.s-plus.com. 2 Jan 2013
  11. 11.
    Matlab. Wavelet toolbox. www.matlab.com. 2 Jan 2013
  12. 12.
    ION Script (2004) Wavelets. ION script user’s guide. Edit. by Research Systems, BoulderGoogle Scholar
  13. 13.
    Ishikawa Y (2001) Wavelet analysis for clinical medicine. Edit. by Med Pub, Igaku-Shuppan, JapanGoogle Scholar
  14. 14.
    Suarez L, Barrett-Connor E (1982) Seasonal variation in fasting plasma glucose levels in man. Diabetology 22:250–253CrossRefGoogle Scholar
  15. 15.
    Barrett-Connor E (1980) Factors associated with the distribution of fasting plasma glucose in an adult community. Am J Epidemiol 112:518–523PubMedGoogle Scholar
  16. 16.
    Marmor T, Oberlander J, White J (2009) The Obama administration’s options for health care cost control: hope versus reality. Ann Intern Med 150:485–489PubMedCrossRefGoogle Scholar
  17. 17.
    Cleophas TJ, Zwinderman AH (2012) More on non linear relationships, splines. In: Statistics applied to clinical studies, 5th edn. Springer, Dordrecht, pp 277–288CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ton J. Cleophas
    • 1
  • Aeilko H. Zwinderman
    • 2
  1. 1.SliedrechtThe Netherlands
  2. 2.Department of Epidemiology and BiostatisticsAcademic Medical CenterAmsterdamThe Netherlands

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