Solving Fourier Transform Problem: f(x) = e^(-pi*x^2)

[galipop]

Hi All,

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

 

[arildno]

1. You should first of all "complete the square" in the exponent.
2. If you've done that, and still got problems about how to evaluate the expression, try to explain what your problem is precisely.

 

[Dr Transport]

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

 

[galipop]

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

 

[galipop]

I have another problem to solve, but it looks similar to the one above.

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

 

[arildno]

Note that you easily may replace f with some derivative, dG/dx.
Use the product rule for integration to compute the answer.