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Finite Fourier Transform on a 3d wave

  1. Sep 16, 2013 #1
    Finite Fourier Transform on a 2d wave

    How does the finite fourier transform work exactly?

    The transform of f(x) is
    [itex]\widetilde{f}(\lambda_{n})[/itex] =[itex]\int[/itex][itex]^{L}_{0}[/itex] f(x) X[itex]_{n}[/itex] dx

    If I had a 3d wave equation pde and I applied Finite fourier transform on the pde for
    z(x,y,t)=X(x)Y(y)T(t)

    f(x)=z[itex]_{xx}[/itex]
    [itex]\tilde{z_{xx}(\lambda_{n})}[/itex] =[itex]\int[/itex][itex]^{L}_{0}[/itex] z[itex]_{xx}[/itex] X[itex]_{n}[/itex](x) dx

    f(x)=z[itex]_{yy}[/itex]
    [itex]\tilde{z_{yy}(\lambda_{n})}[/itex] =[itex]\int[/itex][itex]^{L}_{0}[/itex] z[itex]_{yy}[/itex] Y[itex]_{n}[/itex](y) dy

    etc for T

    or

    is the transform the same for everything, namely:
    f(x)=z[itex]_{xx}[/itex]
    [itex]\tilde{z_{xx}(\lambda_{n})}[/itex] =[itex]\int[/itex][itex]^{L}_{0}[/itex] z[itex]_{xx}[/itex] X[itex]_{n}[/itex](x) Y[itex]_{n}[/itex](y) dx

    or is it a double integral?
    or do you apply finite fourier twice with respect to y and x.
     
    Last edited: Sep 16, 2013
  2. jcsd
  3. Sep 16, 2013 #2

    I like Serena

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    Homework Helper

    Hi brandy! :smile:

    You can take any transform you want, including a 3D fourier transform, which would be a triple integral.
    And also a transform of for instance ##z_{xx}## with respect to y.

    In all cases you can apply the Fourier's theorems.
    It's just a matter of what you want to achieve.
     
  4. Sep 16, 2013 #3

    jasonRF

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    Note that you should have a different "frequency" variable for each dimension $x$ and $y$.
     
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