IEVref:103-04-01ID:
Language:enStatus: Standard
Term: Fourier transform
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Definition: 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 −jω t 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.


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