Basic Examples

Here are some of the transforms we did in class.

In[2]:=

  FourierTransform[DiracDelta[t],t,w]

Out[2]=

In[3]:=

  FourierTransform[UnitStep[t+L]-UnitStep[t-L],t,w]

Out[3]=

  2 Sin[L w]
  ----------
      w

In[4]:=

  FourierTransform[Exp[- a t]UnitStep[t],t,w]

Out[4]=

     1
  -------
  a - I w

In[5]:=

  FourierTransform[Exp[- a t^2],t,w]

Out[5]=

      Sqrt[Pi]
  -----------------
            2
           w /(4 a)
  Sqrt[a] E

In[6]:=

  FourierTransform[1/(3+I t),t,w]

Out[6]=

  2 Pi UnitStep[w]
  ----------------
         3 w
        E

In[7]:=

  InverseFourierTransform[1,w,t]

Out[7]=

  DiracDelta[t]