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I was reviewing a homework problem, and I'm trying to figure this out.

The Fourier transform of ${1\over 2} cos(3\pi t)$, according to the solution I was given is ${1\over 2}\{\delta(f+{2\over 3})+\delta(f-{2\over 3})\}$. Wolfram Alpha, however, gives $\sqrt{\pi\over2} \delta(f-3 \pi)+\sqrt{\pi\over2} \delta(f+3 \pi)$. Is the solution I was given the correct one? I don't think Alpha is using $\omega$ (angular frequency, equal to $2\pi f$) in the calculation. That might be where I'm getting confused here.

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I think Fourier Transform, in general, can be defined in various ways. Please check the definition your book or you teacher used, with the one that wolfram uses here: http://reference.wolfram.com/mathematica/ref/FourierTransform.html

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  • $\begingroup$ Mathematica is using angular frequency. When I type the function into Mathematica using FourierTransform[1/2*Cos[3*pi*t], t, f], I get the same answer that Wolfram Alpha gives me. Was I given a faulty solution? $\endgroup$ – user116297 Dec 17 '13 at 17:16

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