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Fourier transform of a gaussian

  1. Oct 20, 2009 #1
    fourier transform of the gaussian (1/[tex]\sqrt{2 pi \sigma}[/tex]) e ^ ([tex]^{x^2/2\sigma^2}[/tex])



    now the fourier of a gaussian is said to equal another gaussian as shown by equation (4) here:
    http://mathworld.wolfram.com/FourierTransform.html

    but when i also did it using equation (1) here:
    http://mathworld.wolfram.com/FourierTransform.html

    i find a completely different answer.

    im wondering how i am doing the calculations wrong using the normal definition of fourier transforms.

    fourier transforms are very new to me so any help is much appreciated thank you.
     
  2. jcsd
  3. Oct 21, 2009 #2

    lanedance

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    Homework Helper

    you'll have more chance if you show you working, its pretty hard to guess what you're doing wrong
     
  4. Oct 21, 2009 #3
    setting a=1/2 [tex]\sigma[/tex] ^2 and k=1/2[tex]\sqrt{2 pi sigma}[/tex] i use the concept the fourier of a gaussian equals another gaussian and am given
    [tex]\sqrt{2 sigma ^2 pi}[/tex] e^((-2pi^2 [tex]\sigma[/tex]^2 / [tex]\sqrt{2 pi sigma}[/tex]
     
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