# [✓] Get the FourierTransform of a two dimension door function?

GROUPS:
 Please did you can help me to make the foueeir transform of two dimension door function FourierTransform[Piecewise[{{1, x^2 + y^2 <= 1}, {0, x^2 + y^2 > 1}}], {x, y}, {u, v}] When i make the previous commande, i can't have anay result Thank you
 Michael Helmle 1 Vote Your code works for me: \$Version (* "11.1.0 for Microsoft Windows (64-bit) (March 13, 2017)"*) f1 = FourierTransform[ Piecewise[{{1, x^2 + y^2 <= 1}, {0, x^2 + y^2 > 1}}], {x, y}, {u, v}] (* BesselJ[1,Sqrt[u^2+v^2]]/Sqrt[u^2+v^2]*) Plot3D[f1, {u, -7, 7}, {v, -7, 7}, PlotRange -> All] 
 Hi Abdelkarim,the Fourier transform of a rotational symmetric function is basically a Hankel transform. In the 2D case it is a Hankel transform of order 0. So here we simply can calculate: HankelTransform[HeavisideTheta[1 - r], r, \[Rho]] which gives an immediate result in terms of a Bessel function.Regards -- HenrikEdit:@Michael Helmle : Sorry, I did not see your answer - which I prefer! I was thinking more in terms of mathematics than of Mathematica ...