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First a warning: my Mathematica skills, and computery-type skills in general, are not very hot. My problem is thus: I have a function which I know:

[tex] \hat{f}(k) [/tex]

I'd like mathematica to approximate the inverse Fourier transform of this function for me and plot the result. I've tried using the built-in function "NInverseFourierTransform", but it fails to produce meaningful results. My function oscillates quite rapidly, so NIntegrate doesn't work too well.

Now I'm aware that I could approximate the inverse Fourier transform using a discrete Fourier transform and the FFT algorithm - but I'm afraid I don't really know how to go about doing it. I can do the following:

- Get as many sample points of [tex]\hat{f}(k)[/tex] as you want. Call them [tex]\{\hat{f}_n\}[/tex].
- I can make [tex]\hat{f}[/tex] rapidly decreasing, so it's pretty much got compact support.
- My [tex]\hat{f}[/tex] is smooth.

- , where list contains the [tex]\hat{f}_n[/tex], and plotting the real part of it, but the answer is gibberish. I've proved lots of rigorous results regarding the function [tex]f[/tex], so I
*know*(pretty much) what the plot of the inverse Fourier transform should look like!

If anyone could help me implement the built in mathematica functions to get a plot of this inverse Fourier transform, I'd be immensely grateful.

Thanks,

Ant