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Fourier Transform stumped

  1. Mar 13, 2004 #1
    Hi all, I had this problem for homework and it stumped me. It's too late to get points for it, but I'd like to know for future reference. I posted in the homework help forum but figured I'd try here too.

    Find the Fourier transform F(w)=integral from -infinity to infinity of f(t)e^(i*w*t)dt

    f(t)=e^(-t^2/a^2)

    i=sqrt(-1) w=omega=constant a=constant

    This looks sort of like a gaussian integral:

    integral of e^(-a*x^2)dx=sqrt(pi/a)

    but I couldn't see how to do it...

    The answer given by the book is sqrt(pi)ae^(-a^2*w^2/4)

    Anyone know how to do this??
     
  2. jcsd
  3. Mar 13, 2004 #2

    arildno

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    Complete the square..
     
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