In[]:=
LT[f_,t_,s_]:=
∞
∫
-∞
f
-st

t
In[]:=
f[t_]:=Piecewise[{{1,-3<t<4}}]
In[]:=
Plot[f[t],{t,-5,7}]
Out[]=
In[]:=
F=LT[f[t],t,s]
In[]:=
-4s

(-1+
7s

)
s
In[]:=
Block[{s=σ+Iω},Table[plot[Abs[F],{σ,-20,20},{ω,-20,20},PlotRangeFull],{plot,{Plot3D,ContourPlot,DensityPlot}}]]
Out[]=

,
,

​
​