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Fourier Transform

  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.

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


    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
    I think the thing you want to do here is complete the square in the arguements of the exponential. In this expression:
    -t^2/a^2 + iwt = -(t-b)^2 +c.
    where you can find b and c. When you've done that you can change variables and you will have and expression for the Gaussian that you are familiar with.
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