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Area Mathematics - Functions / Integral transformations

IEV ref103-04-01

en
Fourier transform
for a real or complex function f(t) of the real variable t, complex function F(ω) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAeacaGGOaGaeq yYdCNaaiykaaaa@3941@ of the real variable ω, given by the integral transformation

F(ω)= + f(t) e jωt dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAeacaGGOaGaeq yYdCNaaiykaiabg2da9maapedabaGaamOzaiaacIcacaWG0bGaaiyk aKqzafGaaiyzaOWaaWbaaSqabeaacqGHsislcaqGQbGaeqyYdCNaaG jcVlaadshaaaqcLbuaciGGKbGccaWG0baaleaacaaMi8UaeyOeI0Ia eyOhIukabaGaaGjcVlabgUcaRiabg6HiLcqdcqGHRiI8aaaa@521C@

where j is the imaginary unit

Note 1 to entry: If t is time, the variable ω represents angular frequency.

Note 2 to entry: The Fourier transform of the function f is also denoted Ff or ℱf.


fr
transformée de Fourier, f
pour une fonction réelle ou complexe f(t) de la variable réelle t, fonction complexe F(ω) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAeacaGGOaGaeq yYdCNaaiykaaaa@3941@ de la variable réelle ω, donnée par la transformation intégrale

F(ω)= + f(t) e jωt dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAeacaGGOaGaeq yYdCNaaiykaiabg2da9maapedabaGaamOzaiaacIcacaWG0bGaaiyk aKqzafGaaiyzaOWaaWbaaSqabeaacqGHsislcaqGQbGaeqyYdCNaaG jcVlaadshaaaqcLbuaciGGKbGccaWG0baaleaacaaMi8UaeyOeI0Ia eyOhIukabaGaaGjcVlabgUcaRiabg6HiLcqdcqGHRiI8aaaa@521C@

où j est l’unité imaginaire

Note 1 à l'article: Si t est le temps, la variable ω représente la pulsation.

Note 2 à l'article: La transformée de Fourier de la fonction f est notée aussi Ff ou ℱf.


ar
تحويل فورير

de
Fourier-Transformierte, f

es
transformada de Fourier

it
trasformata di Fourier

ja
フーリエ変換, 動詞

pl
transformata Fouriera

pt
transformada de Fourier

sr
Фуријеова трансформација, ж јд

sv
fouriertransform

zh
傅里叶变换, <相关条目:103-04-02>

Publication date: 2009-12
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