# What should I expect for Fourier transform of Sinc? [closed]

I was expecting something I could interpret as a rect function. I don't think the Dirac delta function qualifies — for one thing, I think that would be the transform of a constant.

FourierTransform[Sinc[t], t, ω]

2.50245 DiracDelta[ω]


Is there a way to make sense of this?

I'm using v.9.0 home

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## closed as off-topic by Szabolcs, m_goldberg, bobthechemist, rasher, Michael E2Jun 15 at 4:47

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• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Szabolcs, m_goldberg, bobthechemist, rasher, Michael E2
If this question can be reworded to fit the rules in the help center, please edit the question.

It is likely that some of the variables you use here have assigned values. I cannot reproduce this result and there's no other explanation of why there's an inexact number in the result (!!): 2.50245 Restart the kernel (Quit), then try again. I get 1/2 Sqrt[\[Pi]/2] (Sign[1 - \[Omega]] + Sign[1 + \[Omega]]). –  Szabolcs Jun 15 at 1:28
@Szabolcs: thank you, I have no idea how that happened but you are right. –  daniel Jun 15 at 1:30
You didn't notice because there's special syntax colouring in FourierTransform and the variables with values did not show as black. Sometimes syntax colouring works against us. –  Szabolcs Jun 15 at 1:32

\$Version


"9.0 for Mac OS X x86 (64-bit) (January 24, 2013)"

ft[w_] = FourierTransform[Sinc[t], t, w]


(1/2)Sqrt[Pi/2](Sign[1 - w] + Sign[1 + w])

Plot[ft[w], {w, -2, 2}, PlotStyle -> Directive[Red, Thick]]


InverseFourierTransform[ft[w], w, t] == Sinc[t] // FullSimplify


True

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