In wikipedia's Fourier Transform site there are tables of important FTs, the thing is that Mathematica always considers angular frequency. Is there a way to get what is in the second column labeled Fourier transform, unitary, ordinary frequency?


One way is to adjust the FourierParameters

  FourierTransform[1, x, w, FourierParameters -> {0, -2*Pi}]

Mathematica graphics

  FourierTransform[Exp[I a x], x, w, FourierParameters -> {0, -2*Pi}]

Mathematica graphics


funs = {1, DiracDelta[x], Exp[I a x], Cos[a x], Sin[a x]};
result= {#, FourierTransform[#, x, w, FourierParameters -> {0, -2*Pi}]}& /@ funs;
Prepend[result, {"f(x)","Fourier transform unitary, ordinary frequency"}];
Grid[%, Frame -> All]

Mathematica graphics

With Wiki's second column:

Mathematica graphics

  • 1
    $\begingroup$ Thanks, why is it between 0 and negative 2pi instead of just 2pi? $\endgroup$
    – vlizana
    Sep 12 '19 at 5:04
  • 2
    $\begingroup$ @vlizana Guessing the meaning of an option should always be the last thing to do. FourierParameters -> {0, -2*Pi} doesn't mean "between 0 and negative 2pi", please check Details and Options section of document of FourierTransform by pressing F1. $\endgroup$
    – xzczd
    Sep 12 '19 at 10:18
  • $\begingroup$ But I can't seem to find in the docs the exact meaning of these parameters, it only shows which should be used for "pure mathematics", "modern" and "classical physics" but it does not show any explanation on where do they come in on the formula or anything, $\endgroup$
    – vlizana
    Sep 12 '19 at 21:06

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