Calculating 3D Fourier Transform for (1,2,3)

[PianoDentist]

Hi, just got set a 3d Fourier transform to solve but I've never seen one before and can't find any examples online. once the integral is set up I should be fine but I'm not sure how to set it up;

What is Fourier transfrom (f(k)) of following 3d function for k=(k_x, k_y, k_z)=(1,2,3)

for f(x,y,z) = 1 if mod(x)<1,mod(y)<1,mod(z)<1 and f(x,y,z)=0 otherwise

Im just struggling how to set up the integral, I assume I have to do a triple integral, but I am not sure whether I have to simply integrate from -1 to 1 for x,y and z (here I am not sure what to do with what's normally e^(-ikx))...or whether I have to convert to spherical co-ordinates.

any help would be greatly appreciated

 

[Dick]

Yes, just integrate from -1 to 1 for x,y and z. Spherical coordinates wouldn't help. And kx is the dot product of the vector k and the vector x=(x,y,z).