Anthony
May14-09, 04:45 PM
Hi all,
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:
\hat{f}(k)
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 \hat{f}(k) as you want. Call them \{\hat{f}_n\}.
I can make \hat{f} rapidly decreasing, so it's pretty much got compact support.
My \hat{f} is smooth.
I figure if I've got the above properties, there must be some way of approximating the inverse Fourier transform using the built in FFT functions in mathematica. I've tried using InverseFourier[list], where list contains the \hat{f}_n, and plotting the real part of it, but the answer is gibberish. I've proved lots of rigorous results regarding the function f, 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
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:
\hat{f}(k)
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 \hat{f}(k) as you want. Call them \{\hat{f}_n\}.
I can make \hat{f} rapidly decreasing, so it's pretty much got compact support.
My \hat{f} is smooth.
I figure if I've got the above properties, there must be some way of approximating the inverse Fourier transform using the built in FFT functions in mathematica. I've tried using InverseFourier[list], where list contains the \hat{f}_n, and plotting the real part of it, but the answer is gibberish. I've proved lots of rigorous results regarding the function f, 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