# FourierTransform frequency

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}]


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


Compare

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]


With Wiki's second column:

• Thanks, why is it between 0 and negative 2pi instead of just 2pi? – vlizana Sep 12 '19 at 5:04
• @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. – xzczd Sep 12 '19 at 10:18
• 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, – vlizana Sep 12 '19 at 21:06