Considering Sam's input, and the sketch above, would the following work?
T = 4;
g[t_] := Sinc[T t];
f[\[Omega]_] := FourierTransform[ g[t], t, \[Omega], FourierParameters -> {1,-1} ]
plt0 = Plot[ g[t], {t, -2T, 2T}, AxesLabel -> {Automatic, "g(t)"},
PlotRange -> {{-2T, 2T},All} ,
PlotStyle -> {Thick, Red, Dashed}];
plt1 = Plot[ f[\[Omega]], {\[Omega], -2T, 2T}, AxesLabel -> {Automatic,"F(\[Omega])"},
PlotRange -> {{-2T, 2T},All} ,
PlotStyle -> {Thick, Blue}];
Show[ {plt0,plt1},
AxesLabel -> {"","g(t), F(\[Omega])"},
(* Change Ticks to None to have no markers *)
Ticks -> {Automatic, Automatic}]