Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fourier Transform

  1. Apr 26, 2004 #1
    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
     
  2. jcsd
  3. Apr 26, 2004 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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.
     
  4. Apr 26, 2004 #3

    Dr Transport

    User Avatar
    Science Advisor
    Gold Member

    The Fourier transform of a gaussian is a gaussian, complete the square and do the integral.
     
  5. Apr 26, 2004 #4
    cheers... once I completed the square it was fairly straight forward.
     
  6. Apr 26, 2004 #5
    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
     
  7. Apr 27, 2004 #6

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Note that you easily may replace f with some derivative, dG/dx.
    Use the product rule for integration to compute the answer.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Fourier Transform Date
I Repetitive Fourier transform Apr 2, 2018
I Units of Fourier Transform Mar 26, 2018
A Help with Discrete Sine Transform Sep 29, 2017
I Motivation for Fourier series/transform Oct 17, 2016