Computational Complexity

2012 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Comparison of Discrete and Continuous Wavelet Transforms

  • Palle E. T. Jorgensen
  • Myung-Sin Song
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-1800-9_34

Article Outline

Glossary

Definition of the Subject

Introduction

The Discrete vs. Continuous Wavelet Algorithms

List of Names and Discoveries

History

Tools from Mathematics

A Transfer Operator

Future Directions

Literature

Acknowledgments

Bibliography

This glossary consists of a list of terms used inside the paper in mathematics, in probability, in engineering, and, on occasion, in physics. To clarify the seemingly confusing use of up to four different names for the same idea or concept, we have further added informal explanations spelling out the reasons behind the differences in current terminology from neighboring fields.

Disclaimer: This glossary has the structure offour areas. A number of terms are listed line by line, and each line is followed byexplanation. Some “terms” have up to four separate (yet commonly accepted)names.

Keywords

Hilbert Space Wavelet Transform Transfer Operator Wavelet Basis Continuous Wavelet Transform 
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.
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Notes

Acknowledgments

We thank Professors Dorin Dutkay and Judy Packer for helpfuldiscussions.

Work supported in part by the U.S. National Science Foundation.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Palle E. T. Jorgensen
    • 1
  • Myung-Sin Song
    • 2
  1. 1.Department of MathematicsThe University of IowaIowa CityUSA
  2. 2.Department of Mathematics andStatisticsSouthern Illinois UniversityEdwardsvilleUSA