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I've been going through a few Fourier transform problems and I'm stuck with integrating this one:

f(x) = e^(-pi*x^2)

then

F(e^(-pi*x^2)) = integral (e^(-pi*x^2) * e^(-i*w*x)).dx

Can anyone help me out?

Many Thanks,

Pete

- Thread starter galipop
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- #1

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I've been going through a few Fourier transform problems and I'm stuck with integrating this one:

f(x) = e^(-pi*x^2)

then

F(e^(-pi*x^2)) = integral (e^(-pi*x^2) * e^(-i*w*x)).dx

Can anyone help me out?

Many Thanks,

Pete

- #2

arildno

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2. If you've done that, and still got problems about how to evaluate the expression, try to explain what your problem is precisely.

- #3

Dr Transport

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The Fourier transform of a gaussian is a gaussian, complete the square and do the integral.

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cheers... once I completed the square it was fairly straight forward.

- #5

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f(x) = x * e^(-pi*x^2).

So now there is an extra term.

Can I use the result from the previous problem to find the Fourier transform? Any hints to get me started would be greatly appreciated.

Cheers,

Pete

- #6

arildno

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Use the product rule for integration to compute the answer.

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