Fourier transform

  • Thread starter hula
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  • #1
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an equation involves an integration. After an inverse fourier transform of the equation, will the integration limits change? (maybe you can take a look at the attached file)

Thanks!
 

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  • #2
CompuChip
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I can't read your attachment, but I think in general the answer would be yes.
Consider the function
[tex]F(a) = \int_0^a f(x) \, dx[/tex]
The Fourier-transform will be
[tex]\tilde F(k) = \frac{1}{\sqrt{2\pi}} \int e^{-ika} F(a) \, da
= \frac{1}{\sqrt{2\pi}} \int \int_0^a f(x) e^{-ika} \, dx \, da
[/tex]
If you are lucky you will be able to do the integral in a and are left with one other integral, whose boundaries are probably not the same. But of course, if you transform this back, you should get the original function again (otherwise it's not really a good Fourier transform, is it)
 

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