An Introduction to Wavelets

Abstract

Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Wavelets were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, and earthquake prediction. This paper introduces wavelets to the interested technical person outside of the digital signal processing field. I describe the history of wavelets beginning with Fourier, compare wavelet transforms with Fourier transforms, state properties and other special aspects of wavelets, and finish with some interesting applications such as image compression, musical tones, and de-noising noisy data.

Keywords: Wavelets, Signal Processing Algorithms, Orthogonal Basis Functions, Wavelet Applications

Contents:

  1. Overview

  2. Historical Perspective

  3. Sidebar- What are Basis Functions?

  4. Fourier Analysis

  5. Wavelet Transforms versus Fourier Transforms

  6. What Do Some Wavelets Look Like?

  7. Wavelet Analysis

  8. Wavelet Applications


  9. Wavelets Endnote

  10. References

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Copyright Notice

Copyright (c) 1995 by the Institute of Electrical and Electronics Engineers, Inc. Personal use of this material is permitted. However, permission to reprint/republish this material in digital or hard copy form must be obtained from the IEEE. To copy or otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works for any purpose requires prior permission from the IEEE. A fee may be charged for re-use. Abstracting with credit is permitted. Copyrights for components of this work owned by others than IEEE must be honored.

The original version of this work appears in IEEE Computational Science and Engineering, Summer 1995, vol. 2, num. 2, published by the IEEE Computer Society, 10662 Los Vaqueros Circle, Los Alamitos, CA 90720, USA, TEL +1-714-821-8380, FAX +1-714-821-4010.

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Last Modified by Amara Graps on 12 May 2004.
© Copyright Amara Graps, 1995-2004.