omega=0.5

h[n_]:=omega/Pi Sinc[n omega]

draw[J_]:=Plot[Sum[h[n]Exp[-I n t],{n,-J/2,J/2}],{t,-Pi,Pi},PlotRange->All]

draw[100]

Plot[If[Abs[x]≤omega,1,0],{x,-Pi,Pi}]