I want to compute the 2D Fourier transform of the function $circ(\sqrt{(x-a)^2+(y-b)^2})$. Obviously, this is a circle centered at $(a,b)$ and with radius 1, because of the $circ$ function.
How do I compute the Hankel transform of this, since the function is radially symmetric.
I believe that the first step is convert the equation $(x-a)^2+(y-b)^2=1$ to polar coordinates, with the parametrization $x=cos\theta+a$, $y=sin\theta+b$, so you get the familiar trigonometric identity. However I don't understand what to do now, since it seems like the shift in location has disappeared and therefore cannot be reflected in the Hankel transform.
How do I resolve this?