# Fourier transform not working! [closed]

The FourierTransform doesn't seem to work on the following function:

    fun[x_, y_, t_] =
1/((x - 4 y) (x + 4 y) (x^2 + 2 y^2))
E^(-(1/4)
t (3 x + Sqrt[
x^2 - 16 y^2])) (-E^(1/4 t (3 x + Sqrt[x^2 - 16 y^2]))
x^2 (x - 4 y) (x + 4 y) + x^3 Sqrt[x^2 - 16 y^2] -
E^(1/2 t Sqrt[x^2 - 16 y^2]) x^3 Sqrt[x^2 - 16 y^2] +
5 x y^2 Sqrt[x^2 - 16 y^2] -
5 E^(1/2 t Sqrt[x^2 - 16 y^2]) x y^2 Sqrt[
x^2 - 16 y^2] + (1 + E^(1/2 t Sqrt[x^2 - 16 y^2])) (x -
4 y) (x + 4 y) (x^2 + y^2));


Doing FourierTransform[fun[x, y, t], t, \[Omega]] simply returns the same thing (i.e., FourierTransform[expression of the function]. How can I calculate the FourierTransform of this function and plot it?

• Using Expand beforehand might work. May 25, 2021 at 19:34
• Thanks @JulienKluge, it did give an expression. But I am not able to plot it with respect to $\omega$!
– Mike
May 25, 2021 at 19:55
• To plot it, you will need to assign numerical values to x and y. If its imaginary part is non-zero, you will need to convert it to real numbers (e.g. using Abs, Re, Im or ReIm) May 25, 2021 at 19:59
• I tried that in the first place. The problem seems to come from the DiracDelta in the expression of FourierTransform.
– Mike
May 25, 2021 at 20:03
• I think for most of values of x and y that FourierTransform simply does not exist. For example, putting {x -> 1, y -> 1}], we otain a meaningless result -8 I Sqrt[(2 \[Pi])/15] DiracDelta[-3 I + Sqrt - 4 s] + 8/3 Sqrt[2 \[Pi]] DiracDelta[-3 I + Sqrt - 4 s] - 1/3 Sqrt[2 \[Pi]] DiracDelta[s] + 8 I Sqrt[(2 \[Pi])/15] DiracDelta[3 I + Sqrt + 4 s] + 8/3 Sqrt[2 \[Pi]] DiracDelta[3 I + Sqrt + 4 s]. Here s instead of \[Omega] is used. Putting {x -> 5, y -> 1}, one obtains -(25/27) + 76/27 E^(-9 t/2) - (8 E^(-3 t))/9. Its FT does not exist. May 26, 2021 at 5:05