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How to compute multidimensional inverse Fourier transform

  1. Nov 15, 2014 #1
    Hello, everybody. I am currently working on deriving solutions for Stokes flows. I encounter a multidimensional inverse Fourier transform. I already known the Fourier transform of the pressure field:
    [itex]\tilde{p}=-\frac{i}{{{k}^{2}}}\mathbf{F}\centerdot \mathbf{k}[/itex]
    where [itex]i[/itex] is the imaginary unit, [itex]\mathbf{k}[/itex] is the frequency vector, [itex]k[/itex] is the length of [itex]\mathbf{k}[/itex] (That is, [itex]k=\left\| \mathbf{k} \right\|[/itex]), and [itex]\mathbf{F}[/itex] is a constant vector. I don't know how to perform the inverse transform, although I have found the final answer in some references, which reads
    [itex]p=\frac{\mathbf{F}\centerdot \mathbf{x}}{4\pi {{r}^{3}}}[/itex]
    where [itex]r=\left\| \mathbf{x} \right\|[/itex]
    Does anybody has an idea? Thanks a lot.
  2. jcsd
  3. Nov 15, 2014 #2


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    Staff: Mentor

    If you could show what you fear is the problem you have in solving these problems, it could help us understand where you need help.
  4. Nov 16, 2014 #3
    Oh, I have found the answer. It is presented in the following link:
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