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}]