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Fourier Transform

  1. Apr 20, 2006 #1
    ok so here's the question, show explicitly that

    the integral from -inf to inf of |f(k)|^2=1

    where [tex] f(x) = \frac{N}{\sqrt{\sigma}}*e^{\frac{-x^2}{2\sigma^2}} [/tex]
    When doing the integral for the forier transform, I was going to use the gaussian integral to simplify it, but I dont htink I can do that, any ideas?
     
    Last edited: Apr 20, 2006
  2. jcsd
  3. Apr 20, 2006 #2
    I have tried and looked up several methods to solving this awfully ugly integral, anyone have any ideas?
     
  4. Apr 21, 2006 #3

    J77

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    Only a suggesstion - but it looks like you're going to have a situation where:

    limit as [tex]{k\rightarrow\pm \infty}[/tex] of [tex]\frac1{k}e^{-k^2}[/tex] with some constants thrown in...

    my suspicion is that you'll have to use L'Hopital.
     
    Last edited: Apr 21, 2006
  5. Apr 21, 2006 #4

    Hurkyl

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    It is a Gaussian integral...
     
  6. Apr 23, 2006 #5
    Im not sure how it is, I can see that f(x) might be, but not f(K)
     
  7. Apr 23, 2006 #6

    Hurkyl

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    What's the difference between f(x) and f(k)?
     
  8. Apr 23, 2006 #7
    a factor of e^-(pi)*i*k*x
     
  9. Apr 23, 2006 #8
    anyone?


    ......
     
  10. Apr 24, 2006 #9

    HallsofIvy

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    Once again, what's the difference between f(x) and f(k)? f(k) is just f(x) with variable k instead of x!
     
  11. Apr 24, 2006 #10
    I don't see that, I dont understand how the fourier transform just changes the x's to k's.
     
  12. Apr 24, 2006 #11

    nrqed

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    This is a bit confusing. Do you really mean f(k)?? (in which case it is the function you gave with x replaced by k) or do you mean F(k), the Fourier transform of f(x)? (I am assuming that you mean the latter otherwise the question has nothing to do with Fourier transforms and the question is trivial. I think this is what you meant and that the other posters missed).

    well, you have to calculate F(k), the Fourier transform of your f(x) first. Do you know how to calculate a Fourier transform in the first place? If not, you should look up the definition and then ask more questions if thsi is not clear.
     
  13. Apr 24, 2006 #12
    I am given f(k). Nothing else is made clear to me. I do infact know how to do fourier transforms, I do infact could solve the problem if it, or the help i was given hear made any sense.
     
  14. Apr 24, 2006 #13

    shmoe

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    Can you latex what this integral is? I'm confused on where your confusion lies, so knowing what you are staring at would help us out.
     
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