Tagged Questions
2
votes
1answer
336 views
Three Dimensional Fourier Transform of Radial Function without Bessel and Neumann
I am trying to compute the Fourier transform of $\frac1{|\mathbf{x}|^2+1}$ where $\mathbf{x}\in\mathbb{R}^3$.
Just writing out the integral: ...
1
vote
1answer
263 views
What is the generalization of Parseval's theorem into spherical coordinates?
what is the relationship between the total power of a function given in spherical coordinates in the Fourier domain:
$E_k=\int_{\mathbb{R}^3}|F(k,\Theta,\Phi)|^2k^2 \sin(\Theta)\,dk\,d\Theta\, ...
2
votes
0answers
380 views
How do I find the inverse Fourier transform of a function that is separable into a radial and an angular part?
I need to take the inverse Fourier transform of a function that is initially specified in spherical coordinates:
$f(r, \theta, \phi) = \int_{R^3}F(k, ...
1
vote
1answer
680 views
How do I find the Fourier transform of a function that is separable into a radial and an angular part?
how do I find the Fourier transform of a function that is separable into a radial and an angular part:
$f(r, \theta, \phi)=R(r)A(\theta, \phi)$ ?
Thanks in advance for any answers!
7
votes
1answer
2k views
How to perform a Fourier transform in spherical coordinates?
For a function $f(r, \vartheta, \varphi)$ given in spherical coordinates, how can the Fourier transform be calculated best? Possible ideas:
express $(r,\vartheta,\varphi)$ in cartesian coordinates, ...
