A simple example to show the essential steps necessary to find the inverse
transform
f(t)
of
g(w)
is shown in the diagram opposite.
g(w)
can be represented as g(w) = 1 for  W £ w £ + W and g(w) is zero for all other frequencies. 

The inverse transform f(t) can be obtained by substituting g(w) into the equation opposite. 

After substituting g(w) the expression for f(t) becomes. 

When the integral is evaluated and the limits inserted, f(t) reduces to 

Furthur Simplification produces the real sinc function multiplied by the area of the pulse/2p. 
