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Resonance

, Volume 9, Issue 11, pp 10–22 | Cite as

Wavelet transforms: Application to data analysis - I

  • Jatan K. Modi
  • Sachin P. Nanavati
  • Amit S. Phadke
  • Prasanta K. Panigrahi
General Article

Abstract

In this article, we elaborate upon the key ideas underlying the construction of various wavelet basis sets. The roles of translation and scaling, which enable the wavelets to localize variations at desired levels of resolution, are clearly brought out. After explaining the implementation of one dimensional wavelet transform, we illustrate their usefulness through the analysis of a data set.

Keywords

Discrete wavelet transform multi-resolution analysis (MRA) translation scaling Daubechies’ basis sets 

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Suggested Reading

  1. [1]
    S Nanavati and P Panigrahi, Wavelet transform: A new mathematical microscope,Resonance, Vol. 9, No. 3, pp 50–64, March 2004.Google Scholar
  2. [2]
    I Daubechies,Ten Lectures on Wavelets, SIAM, Philadelphia, USA. 1992.Google Scholar
  3. [3]
    B B Hubbard,The World According to Wavelets, 2nd edition, Universities Press (India), Hyderabad, 2003.Google Scholar
  4. [4]
    G B Folland, From Calculus to Wavelets: A New Mathematical Technique,Resonance, Vol. 2, No. 4, pp. 25–37, April 1997. Wavelet Information on Internet (as on March 2004).CrossRefGoogle Scholar
  5. [5]
    http://www.wavelets.org, Wavelet Digest, a portal which keeps the information of latest happenings in this field. Could be subscribed through mail.Google Scholar
  6. [6]
    http://www.public.iastate.edu/~rpolikar/WAVELETS/ WTtutorial.html, A Introductory Tutorial on Wavelets by Robi Poliker.Google Scholar

Copyright information

© Indian Academy of Sciences 2004

Authors and Affiliations

  1. 1.Oharmsinh Desai Institute of TechnologyNadiadIndia
  2. 2.Physical Research LaboratoryAhmedabadIndia
  3. 3.National PARAM Superconducting FacilityCentre for Development of Advanced Computing (C-DAC)PuneIndia

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