Continuous wavelet: Difference between revisions
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{{Short description|Functions used by the continuous wavelet transform}} | {{Short description|Functions used by the continuous wavelet transform}} | ||
In [[Numerical analysis|numerical analysis]], '''continuous [[Wavelet|wavelet]]s''' are functions used by the [[Continuous wavelet transform|continuous wavelet transform]]. These functions are defined as analytical expressions, as functions either of time or of frequency. | In [[Numerical analysis|numerical analysis]], '''continuous [[Wavelet|wavelet]]s''' are functions used by the [[Continuous wavelet transform|continuous wavelet transform]]. These functions are defined as analytical expressions, as functions either of time or of frequency. | ||
Most of the continuous wavelets are used for both wavelet decomposition and composition transforms. That is they are the continuous counterpart of [[Orthogonal wavelet|orthogonal wavelet]]s. | Most of the continuous wavelets are used for both wavelet decomposition and composition transforms. That is they are the continuous counterpart of [[Orthogonal wavelet|orthogonal wavelet]]s.<ref>{{Cite book |url=https://books.google.com/books?id=ERlIzB67I9kC&dq=%22Continuous+wavelet%22+-wikipedia&pg=PA48 |title=Abstract Harmonic Analysis of Continuous Wavelet Transforms |date=2005 |publisher=Springer Science & Business Media |isbn=978-3-540-24259-8 |language=en}}</ref><ref>{{Cite book |last=Bhatnagar |first=Nirdosh |url=https://books.google.com/books?id=c2LRDwAAQBAJ&dq=%22Continuous+wavelet%22+-wikipedia&pg=PR4-IA12 |title=Introduction to Wavelet Transforms |date=2020-02-18 |publisher=CRC Press |isbn=978-1-000-76869-5 |language=en}}</ref> | ||
The following continuous wavelets have been invented for various applications: | The following continuous wavelets have been invented for various applications:<ref>{{Cite book |last1=Combes |first1=Jean-Michel |url=https://books.google.com/books?id=n3DtCAAAQBAJ&q=%22Continuous+wavelet%22+%22morlet%22 |title=Wavelets: Time-Frequency Methods and Phase Space Proceedings of the International Conference, Marseille, France, December 14–18, 1987 |last2=Grossmann |first2=Alexander |last3=Tchamitchian |first3=Philippe |date=2012-12-06 |publisher=Springer Science & Business Media |isbn=978-3-642-75988-8 |language=en}}</ref> | ||
* [[Poisson wavelet]] | * [[Poisson wavelet]] | ||
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==See also== | ==See also== | ||
*[[Wavelet]] | *[[Wavelet]] | ||
==References== | |||
{{reflist}} | |||
[[Category:Continuous wavelets| ]] | [[Category:Continuous wavelets| ]] | ||
Latest revision as of 20:18, 4 July 2025
Short description: Functions used by the continuous wavelet transform
In numerical analysis, continuous wavelets are functions used by the continuous wavelet transform. These functions are defined as analytical expressions, as functions either of time or of frequency. Most of the continuous wavelets are used for both wavelet decomposition and composition transforms. That is they are the continuous counterpart of orthogonal wavelets.[1][2]
The following continuous wavelets have been invented for various applications:[3]
- Poisson wavelet
- Morlet wavelet
- Modified Morlet wavelet
- Mexican hat wavelet
- Complex Mexican hat wavelet
- Shannon wavelet
- Meyer wavelet
- Difference of Gaussians
- Hermitian wavelet
- Beta wavelet
- Causal wavelet
- μ wavelets
- Cauchy wavelet
- Addison wavelet
See also
References
- ↑ (in en) Abstract Harmonic Analysis of Continuous Wavelet Transforms. Springer Science & Business Media. 2005. ISBN 978-3-540-24259-8. https://books.google.com/books?id=ERlIzB67I9kC&dq=%22Continuous+wavelet%22+-wikipedia&pg=PA48.
- ↑ Bhatnagar, Nirdosh (2020-02-18) (in en). Introduction to Wavelet Transforms. CRC Press. ISBN 978-1-000-76869-5. https://books.google.com/books?id=c2LRDwAAQBAJ&dq=%22Continuous+wavelet%22+-wikipedia&pg=PR4-IA12.
- ↑ Combes, Jean-Michel; Grossmann, Alexander; Tchamitchian, Philippe (2012-12-06) (in en). Wavelets: Time-Frequency Methods and Phase Space Proceedings of the International Conference, Marseille, France, December 14–18, 1987. Springer Science & Business Media. ISBN 978-3-642-75988-8. https://books.google.com/books?id=n3DtCAAAQBAJ&q=%22Continuous+wavelet%22+%22morlet%22.
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