# Incorrect output from InverseFourierTransform

Bug introduced in 8.0.4 or earlier and fixed in 9.0.1 or earlier

I am trying to compute the inverse Fourier transform of this expression

fhat[w_] = (Exp[-2*I*w] + Exp[2*I*w])


using

f[x_] = InverseFourierTransform[fhat[w], w, x, FourierParameters -> {1, -1}]


Here, Mathematica correctly returns

DiracDelta[-2 + x] + DiracDelta[2 + x]


However, when (when using Mathematica 8) I try to compute this

fhat[w_] = 5*(Exp[-2*I*w] + Exp[2*I*w])


I get 0 as the inverse Fourier Transform, which is clearly incorrect. The result should be 5*(DiracDelta[-2 + x] + DiracDelta[2 + x]).

Can anyone explain to me this behavior? Do you know a way to circumvent this problem?

• I guess you are in v8? I can reproduce this in this version. v9 and v10 give the correct result. – xzczd Sep 17 '14 at 12:25
• You are right, I am in v8. So I will have to update... Is this a known bug of v8? – Goulifet Sep 17 '14 at 12:26
• I think it's not, at least I can't find an exact duplicate. Here's just a possible related one: mathematica.stackexchange.com/q/34027/1871 – xzczd Sep 17 '14 at 12:33
• This is clearly incorrect behaviour. – djp Feb 26 '15 at 1:19