Continuous wavelet transform: Difference between revisions

Revision as of 15:36, 1 July 2021

Revision as of 23:38, 6 October 2021

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{{Use dmy dates|date=July 2013}}

[[File:Continuous wavelet transform.svg|thumb|320px|right|Continuous [[wavelet]] transform of frequency breakdown signal. Used [[symlet]] with 5 vanishing moments.]]

In [[mathematics]], the '''continuous wavelet transform''' ('''CWT)''') is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the [[Wavelet|waveletswavelet]]s vary continuously.

The continuous wavelet transform of a function <math>x(t)</math> at a scale (a>0) <math>a\in\mathbb{R^{+*}}</math> and translational value <math>b\in\mathbb{R}</math> is expressed by the following integral

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:<math>\psi(t)=w(t)\exp(it) </math>

where <math>w(t)</math> is a window. Such defined wavelet can be called as an analyzing wavelet, because it admits to time-frequency analysis. An analyzing wavelet is unnecessary to be admissible.

==Scale factor==

[[File:Continuous wavelet transform.gif|thumb|300px|right]]