I would like to know if there is a similar function to
$$circ(\sqrt{x^2+y^2})=1 , 0\leq \sqrt{x^2+y^2}\leq 1$$
but with a square domain $0\leq x\leq 1$ and $0\leq y\leq 1$.
If yes, which is its fourier transform?
I know that $\mathscr{F}circ(\sqrt{x^2+y^2})=\frac{J_1(2\pi\sqrt{\xi_x^2+\xi_y^2})}{\sqrt{\xi_x^2+\xi_y^2}}$
Thanks!