Posted by Brad Paul on September 18, 2002 at 17:25:53:
In Reply to: Fourier Transform posted by Tim and Alex on September 18, 2002 at 01:49:08:
: Given g(k) = N/(k^2 + a^2) where N, a are parameters
: and
: inf
: /\
: |
: f(x) = (1/((2*pi)^0.5))*| g(k)exp(ikx) dk
: |
: \/
: -inf
: i.e. f(x) <= F.T. => g(k)
: what is f(x)?
: We get as far as
: I(k) = (N/((2*pi)^0.5)) . ((exp(ikx).arctan(x/a))/a)
: f(x) = I(inf) - I(-inf);
: and we cannot understand the significance.
: Any assistance would be greatly appreciated.
Tim and Alex,
I'm sorry I can't be of more help. But all I have for you is the result.
The Fourier Transform of your g(k) function is:
G(x)=F-1{g(k)}=N (pi/2)1/2 e-a |x| /a
If you find a slick way of getting this result do post it.