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Area Mathematics - Functions / Integral transformations

IEV ref103-04-12

en
continuous wavelet transform
CWT
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.


fr
transformée continue en ondelettes, f
intégrale du produit d'une fonction et d'une ondelette décalée et dilatée ou comprimée

Note 1 à l'article: Pour une fonction f(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcaaaa@388F@ et une ondelette 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@

a est le paramètre d’échelle, b est le paramètre de position et * note le complexe conjugué.

Note 2 à l'article: Une transformée discrète en ondelettes est obtenue en choisissant un nombre fini de valeurs des deux paramètres. La transformée inverse exprime la fonction du temps comme une superposition d'ondelettes.


ar
التحويل الموجى المتصل

de
kontinuierliche Wavelet-Transformierte, f
CWT, Abkürzung

es
transformada continua en ondículas

it
trasformata continua in onda unitaria

ja
連続ウェーブレット変換

pl
transformata falkowa ciągła
CWT (akronim)

pt
transformada contínua em ôndulas
CWT (abreviatura inglesa)

sr
непрекидна таласна трансформација, ж јд
CWT

sv
kontinuerlig vågpakettransform

zh
连续小波变换

Publication date: 2009-12
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