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IEVref:103-04-12ID:
Language:enStatus: Standard
Term: continuous wavelet transform
Synonym1: CWT
Synonym2:
Synonym3:
Symbol:
Definition: integral of the product of a function and a shifted and scaled wavelet

Note 1 to entry: For a function f(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcaaaa@388F@ and a wavelet ψ(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeI8a5jaacIcaca WG0bGaaiykaaaa@3972@ :

C f (a,b)= + f(t) ψ a,b (t)dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadoeadaWgaaWcba GaamOzaaqabaGccaGGOaGaamyyaiaacYcacaWGIbGaaiykaiabg2da 9maapedabaGaamOzaiaacIcacaWG0bGaaiykaaWcbaGaeyOeI0Iaey OhIukabaGaey4kaSIaeyOhIukaniabgUIiYdGccaaMc8UaeqiYdK3a a0baaSqaaiaadggacaGGSaGaamOyaaqaaiabgEHiQaaakiaacIcaca WG0bGaaiykaKqzaeGaciizaOGaamiDaaaa@51E2@

where a is the scale parameter, b is the position parameter, and * denotes the complex conjugate.

Note 2 to entry: A discrete wavelet transform is obtained by choosing a finite number of values of the two parameters. The inverse transform expresses the function of time as a superposition of wavelets.


Publication date:2009-12
Source:
Replaces:
Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO
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