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

Article Outline


Definition of the Subject


The Discrete vs. Continuous Wavelet Algorithms

List of Names and Discoveries


Tools from Mathematics

A Transfer Operator

Future Directions




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.


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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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