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Fourier transform me

  1. Dec 12, 2009 #1
    fourier transform plz help me

    if the fourier transform of f(x,y) is f(u,v) what is the fourier transform of the following:


    plz solve it and help me
  2. jcsd
  3. Dec 12, 2009 #2
    Re: fourier transform plz help me

    Just try substituting these into the definition


    f.e. lets do the first one:



    I'm gonna make the next change of variables:

    The boundaries of the integral remains unchanged, and so does the differential, but we get:


    Notice that [tex]e^{i6u}[/tex] is constant wrt to the integration, so we pull it out and what we have left of the integral is simply the fourier transform of f(x,y) [because x* is just a dummy variable]:


    This technique of variable change is the standard technique to observe how shift & scale of the time-domain (the original function) affects the frequency-domain (its fourier transform).
  4. Dec 12, 2009 #3
    Re: fourier transform plz help me

    i can't understand, plz explain more
    thanks for your attention
  5. Dec 30, 2009 #4
    Re: fourier transform plz help me

    You obviously don't understand simple substitution in integrals, maybe you should brush up on that first.
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