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Bug report: wrong sign in the Fourier transform?

Posted 9 years ago

Dear All,

I hope this is the right place to report a bug in the Wolfram Alpha.

It looks like the Wolfram Alpha produces wrong answer for this question: "Fourier of 1/(t-i)" http://www.wolframalpha.com/input/?i=Fourier+of+1%2F%28t-i%29

It tells me that the Fourier transform of 1/(t-i) is zero for negative frequency, however the correct answer is exactly the opposite -- Fourier transform of 1/(t-i) is zero only for w > 0. (Because the Fourier transform is the integral of exp(-iwt)dt/(f-i) and for w > 0 it should be closed in the lower half of the complex plane which is free of poles in this case, the only pole is t = i).

Maybe the sign of the Fourier transform is defined oppositely in Alpha?

/Alexey

POSTED BY: Alexey Petrenko
2 Replies

Wolfram Alpha is going to use Mathematica for the computation. The documented behavior for Mathematica is quite easy to find by web search. Here is the relevant link.

https://reference.wolfram.com/language/ref/FourierTransform.html

Click on Details and Options opener to see information on definition used and parameter settings.

POSTED BY: Daniel Lichtblau

Dear Daniel,

Many thanks for the quick reply! Sorry for the stupid question. I see now, this is not a bug, the exponent in the Fourier transform is simply exp(+iwt), not exp(-iwt) as I assumed!

Best regards, /Alexey

POSTED BY: Alexey Petrenko
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